References
Published online by Cambridge University Press: 23 November 2018
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Information
- Type
- Chapter
- Information
- Formal Geometry and Bordism Operations , pp. 379 - 400Publisher: Cambridge University PressPrint publication year: 2018
References
Adams, J. F. and Atiyah, M. F.. K-theory and the Hopf invariant. Q. J. Math., 17(1):31–38, 1966. [163]10.1093/qmath/17.1.31CrossRefGoogle Scholar
Ando, M., Blumberg, A, J., Gepner, D., Hopkins, M. J., and Rezk, C.. An ∞-categorical approach to R-line bundles, R-module Thom spectra, and twisted R-homology. J. Topol., 7(3):869–893, 2014. [334]CrossRefGoogle Scholar
Anderson, D. W., Brown, E. H., Jr., and Peterson, F. P.. The structure of the Spin cobordism ring. Ann. Math. (2), 86(2):271–298, 1967. [353]10.2307/1970690CrossRefGoogle Scholar
Atiyah, M. F., Bott, R., and Shapiro, A.. Clifford modules. Topology, 3(suppl. 1):3–38, 1964. [353]CrossRefGoogle Scholar
Adams, J. F.. Vector fields on spheres. Topology, 1(1):63–65, 1962. [39]10.1016/0040-9383(62)90096-4CrossRefGoogle Scholar
Adams, J. F.. On the groups J(X): IV. Topology, 5:21–71, 1966. [148, 161, 163]CrossRefGoogle Scholar
Adams, J. F.. Primitive elements in the K-theory of BSU. Q. J. Math., 27(2):253–262, 1976. [251]10.1093/qmath/27.2.253CrossRefGoogle Scholar
Frank Adams, J.. Maps between classifying spaces: II. Invent. Math., 49(1):1–65, 1978. [306]10.1007/BF01399510CrossRefGoogle Scholar
Adams, J. F. Infinite loop. Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1978. [v, 78]CrossRefGoogle Scholar
Adams, J. F.. Stable homotopy and generalised homology. University of Chicago Press, Chicago, IL, 1995. Reprint of the 1974 original. [x, 43, 85, 94, 95]Google Scholar
Adem, J.. The iteration of the Steenrod squares in algebraic topology. PNAS, 38(8):720–726, 1952. [83]CrossRefGoogle ScholarPubMed
Ando, M., French, C. P., and Ganter, N.. The Jacobi orientation and the two-variable elliptic genus. Algebr. Geom. Topol., 8(1):493–539, 2008. [270]CrossRefGoogle Scholar
Ando, M., Hopkins, M. J., and Rezk, C.. Moments of measures on , with applications to maps between p-adic K-theory spectra. Unpublished. [344]Google Scholar
Ando, M., Hopkins, M. J., and Rezk, C.. Multiplicative orientations of ko-theory and the spectrum of topological modular forms. www.math.illinois.edu/∼mando/papers/koandtmf .pdf, accessed: November 16, 2016. [335, 336, 338, 343, 346]Google Scholar
Ando, M., Hopkins, M. J., and Strickland, N. P.. Elliptic spectra, the Witten genus and the theorem of the cube. Invent. Math., 146(3):595–687, 2001. [4, 226, 227, 228, 232, 235, 237, 241, 250, 251, 252, 253, 266, 267, 269, 351]10.1007/s002220100175CrossRefGoogle Scholar
Ando, M., Hopkins, M. J., and Strickland, N. P.. The sigma orientation is an H∞ map. Amer. J. Math., 126(2):247–334, 2004. [66, 78, 317, 319, 322]10.1353/ajm.2004.0008CrossRefGoogle Scholar
Angeltveit, V. and Lind, J. A.. Uniqueness of BP〈n〉. J. Homotopy Relat. Struct., 12(1):17–30, 2017. [194]CrossRefGoogle Scholar
Ando, M. and Morava, J.. A renormalized Riemann–Roch formula and the Thom isomorphism for the free loop space. In Topology, geometry, and algebra: interactions and new directions (Stanford, CA, 1999), pages 11–36. American Mathematical Society, Providence, RI, 2001. [270]10.1090/conm/279/04552CrossRefGoogle Scholar
Amitsur, S. A.. Simple algebras and cohomology groups of arbitrary fields. Trans. Amer. Math. Soc., 90:73–112, 1959. [100]CrossRefGoogle Scholar
Ando, M., Morava, J., and Sadofsky, H.. Completions of Z/(p)-Tate cohomology of periodic spectra. Geom. Topol., 2(1):145–174, 1998. [356]CrossRefGoogle Scholar
Ando, M.. Isogenies of formal group laws and power operations in the cohomology theories En. Duke Math. J., 79(2):423–485, 1995. [319, 320, 321]10.1215/S0012-7094-95-07911-3CrossRefGoogle Scholar
Adams, J. F. and Priddy, S. B.. Uniqueness of BSO. Math. Proc. Cambridge Philos. Soc., 80(3):475–509, 1976. [251, 340]CrossRefGoogle Scholar
Araki, S.. Typical formal groups in complex cobordism and K-theory. Kinokuniya Book-Store Co., Ltd., Tokyo, 1973. [112, 125]Google Scholar
Ando, M. and Strickland, N. P.. Weil pairings and Morava K-theory. Topology, 40(1):127–156, 2001. [227, 232, 236, 241, 242, 243, 244, 246, 247]10.1016/S0040-9383(99)00057-9CrossRefGoogle Scholar
Atiyah, M. F.. Thom complexes. Proc. Lond. Math. Soc., 3(1):291–310, 1961. [357]10.1112/plms/s3-11.1.291CrossRefGoogle Scholar
Baez, J.. Euler characteristic versus homotopy cardinality. Lecture at the Program on Applied Homotopy Theory, Fields Institute, Toronto, September, 2003. [368]Google Scholar
Baker, A.. Combinatorial and arithmetic identities based on formal group laws. In Algebraic Topology Barcelona 1986, pages 17–34. New York: Springer, 1987. [112]CrossRefGoogle Scholar
Baker, A.. Power operations and coactions in highly commutative homology theories. Publ. Res. Inst. Math. Sci., 51(2):237–272, 2015. [309]10.4171/prims/154CrossRefGoogle Scholar
Balmer, P.. Spectra, spectra, spectra: tensor triangular spectra versus Zariski spectra of endomorphism rings. Algebr. Geom. Topol., 10(3):1521–1563, 2010. [154, 155]CrossRefGoogle Scholar
Barthel, T.. Chromatic completion. http://people.mpim-bonn.mpg.de/tbarthel/CC.pdf, accessed: October 26, 2016. [158]Google Scholar
Bauer, T.. Computation of the homotopy of the spectrum tmf . ArXiv Mathematics e-prints, November 2003. [333]Google Scholar
[BCG+ 88] Baker, A., Carlisle, D., Gray, B., Hilditch, S., Ray, N., and Wood, R.. On the iterated complex transfer. Math. Z., 199(2):191–207, 1988. [374]CrossRefGoogle Scholar
Bendersky, M., Curtis, E. B., and Miller, H. R.. The unstable Adams spectral sequence for generalized homology. Topology, 17(3):229– 248, 1978. [169, 171, 177, 178]CrossRefGoogle Scholar
Beilinson, A. A. and Drinfeld, V.. Quantization of Hitchin’s integrable system and Hecke eigensheaves. www.math.uchicago.edu/∼mitya/langlands/hitchin/BD-hitchin.pdf, accessed July 20, 2018. [54]Google Scholar
Beaudry, A.. The chromatic splitting conjecture at n = p = 2. ArXiv e-prints, February 2015. [363]Google Scholar
Beardsley, J.. Constructions of MU by attaching Ek -cells in odd degrees. ArXiv e-prints, August 2017. [360]Google Scholar
Behrens, M.. A modular description of the K (2)-local sphere at the prime 3. Topology, 45(2):343–402, 2006. [366]CrossRefGoogle Scholar
Behrens, M.. Root invariants in the Adams spectral sequence. Trans. Amer. Math. Soc., 358(10):4279–4341, 2006. [358]10.1090/S0002-9947-05-03773-6CrossRefGoogle Scholar
Behrens, M.. Buildings, elliptic curves, and the K (2)-local sphere. Amer. J. Math., 129(6):1513–1563, 2007. [366]CrossRefGoogle Scholar
Behrens, M.. Congruences between modular forms given by the divided β family in homotopy theory. Geom. Topol., 13(1):319–357, 2009. [366]CrossRefGoogle Scholar
Behrens, M.. The homotopy groups of SE(2) at p ≥ 5 revisited. Adv. Math., 230(2):458–492, 2012. [366]CrossRefGoogle Scholar
Behrens, M.. The construction of tmf . In Topological modular forms, pages 149–206. American Mathematical Society, Providence, RI, 2014. [284, 323, 325, 326, 327, 328, 329, 330, 331]Google Scholar
Beilinson, A.A.. Residues and adeles. Functional Analysis and Its Applications, 14(1):34–35, 1980. [164]10.1007/BF01078412CrossRefGoogle Scholar
Barthel, T. and Frankland, M.. Completed power operations for Morava E-theory. Algebr. Geom. Topol., 15(4):2065–2131, 2015. [103]CrossRefGoogle Scholar
Boardman, J. M., Johnson, D.C., and Wilson, W. S.. Unstable operations in generalized cohomology. In Handbook of algebraic topology, pages 687–828. North-Holland, Amsterdam, 1995. [170, 176, 187]CrossRefGoogle Scholar
Buchstaber, V. and Lazarev, A.. Dieudonné modules and p-divisible groups associated with Morava K-theory of Eilenberg–Mac Lane spaces. Algebr. Geom. Topol., 7:529–564, 2007. [207]10.2140/agt.2007.7.529CrossRefGoogle Scholar
Behrens, M. and Laures, G.. β-family congruences and the f -invariant. Geom. Topol. Monographs, 16:9–29, 2009. [281]CrossRefGoogle Scholar
Behrens, M. and Lawson, T.. Topological automorphic forms. Mem. Amer. Math. Soc., 204(958):xxiv–141, 2010. [326, 373]Google Scholar
Baas, N.A. and Madsen, I.. On the realization of certain modules over the Steenrod algebra. Mathematica Scandinavica, 31(1):220–224, 1973. [159]10.7146/math.scand.a-11427CrossRefGoogle Scholar
Bahri, A. P. and Mahowald, M. E.. A direct summand in H∗ (MO〈8〉, Z2). Proc. Amer. Math. Soc., 78(2):295–298, 1980. [351]Google Scholar
Bruner, R. R., May, J. P., McClure, J. E., and Steinberger, M.. H∞ ring spectra and their applications. Springer-Verlag, Berlin, 1986. [75, 76, 77, 78, 83, 148, 164, 284, 319]10.1007/BFb0075405CrossRefGoogle Scholar
J. Boardman, M.. The eightfold way to BP-operations or E∗ E and all that. In Current trends in algebraic topology, Part 1 (London, Ont., 1981), pages 187–226. American Mathematical Society, Providence, RI, 1982. [105]Google Scholar
J. Boardman, M.. Conditionally convergent spectral sequences. In Homotopy invariant algebraic structures (Baltimore, MD, 1998), pages 49–84. American Mathematical Society, Providence, RI, 1999. [104]CrossRefGoogle Scholar
Bousfield, A. K.. The localization of spaces with respect to homology. Topology, 14:133–150, 1975. [309]10.1016/0040-9383(75)90023-3CrossRefGoogle Scholar
Bousfield, A. K.. The localization of spectra with respect to homology. Topology, 18(4):257–281, 1979. [104, 110, 155]CrossRefGoogle Scholar
Bousfield, A. K.. On λ-rings and the K-theory of infinite loop spaces. K-Theory, 10(1):1–30, 1996. [309, 372]CrossRefGoogle Scholar
Barnes, D., Poduska, D., and Shick, P.. Unstable Adams spectral sequence charts. In Adams memorial symposium on algebraic topology: Manchester 1990, volume 2, page 87. Cambridge University Press, Cambridge, 1992. [168]Google Scholar
Breen, L.. Fonctions thêta et théorème du cube. Springer-Verlag, Berlin, 1983. [262, 272]10.1007/BFb0065683CrossRefGoogle Scholar
Browder, W.. The Kervaire invariant of framed manifolds and its generalization. Ann. Math. (2), 90(2):157–186, 1969. [164]10.2307/1970686CrossRefGoogle Scholar
Barthel, T. and Stapleton, N.. The character of the total power operation. Geom. Topol., 21(1):385–440, 2017. [291]10.2140/gt.2017.21.385CrossRefGoogle Scholar
Barthel, T., Schlank, T., and Stapleton, N.. Chromatic homotopy theory is asymptotically algebraic. ArXiv e-prints, November 2017. [367]Google Scholar
Butowiez, J.Y. and Turner, P.. Unstable multiplicative cohomology operations. Q. J. Math., 51(4):437–449, 2000. [165]CrossRefGoogle Scholar
Cartier, P.. Quantum mechanical commutation relations and theta functions. In Proc. Sympos. Pure Math, 9: 361–383, 1966. [260]CrossRefGoogle Scholar
Conner, P. E. and Floyd, E. E.. The relation of cobordism to K-theories. Springer-Verlag, Berlin, 1966. [146, 354]CrossRefGoogle Scholar
Chan, K.. A simple proof that the unstable (co)-homology of the Brown–Peterson spectrum is torsion free. J. Pure Appl. Algebra, 26(2):155–157, 1982. [193]10.1016/0022-4049(82)90020-2CrossRefGoogle Scholar
Clausen, D. and Mathew, A.. A short proof of telescopic Tate vanishing. Proc. Amer. Math. Soc., 145(12):5413–5417, 2017. [345]CrossRefGoogle Scholar
Cohen, R. L.. Odd primary infinite families in stable homotopy theory. Mem. Amer. Math. Soc., 30(242):viii–92, 1981. [211]Google Scholar
Davis, D. M.. Computing v1-periodic homotopy groups of spheres and some compact Lie groups. In Handbook of algebraic topology, pages 993–1048. North-Holland, Amsterdam, 1995. [309]10.1016/B978-044481779-2/50021-3CrossRefGoogle Scholar
Deligne, P.. Cristaux ordinaires et coordonnées canoniques. In Algebraic surfaces (Orsay, 1976–78), pages 80–137. Springer, Berlin, 1981. [326]Google Scholar
Demazure, M.. Lectures on p-divisible groups. Springer-Verlag, Berlin, 1986. Reprint of the 1972 original. [197, 221, 226]Google Scholar
Devalapurkar, S. K.. Roots of unity in K (n)-local E∞ -rings. arXiv preprint arXiv:1707.09957, 2017. [372]Google Scholar
Demazure, M. and Gabriel, P.. Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs. Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam, 1970. [275]Google Scholar
Devinatz, E. S. and Hopkins, M. J.. The action of the Morava stabilizer group on the Lubin–Tate moduli space of lifts. Amer. J. Math., 117(3):669–710, 1995. [160, 202]10.2307/2375086CrossRefGoogle Scholar
Douglas, C. L. and Henriques, A. G.. Topological modular forms and conformal nets. In Mathematical foundations of quantum field theory and perturbative string theory, pages 341–354. American Mathematical Society, Providence, RI, 2011. [377]10.1090/pspum/083/2742433CrossRefGoogle Scholar
Devinatz, E. S., Hopkins, M. J., and Smith, J. H.. Nilpotence and stable homotopy theory: I. Ann. Math. (2), 128(2):207–241, 1988. [148, 360]10.2307/1971440CrossRefGoogle Scholar
Davis, D. G. and Lawson, T.. Commutative ring objects in pro-categories and generalized Moore spectra. Geom. Topol., 18(1):103–140, 2014. [156]10.2140/gt.2014.18.103CrossRefGoogle Scholar
Elmendorf, A. D., Kriz, I., Mandell, M. A., and May, J. P.. Rings, modules, and algebras in stable homotopy theory. American Mathematical Society, Providence, RI, 1997. [74, 102, 283, 343]Google Scholar
Fox, T. F.. The construction of cofree coalgebras. J. Pure Appl. Algebra, 84(2):191–198, 1993. [186]10.1016/0022-4049(93)90038-UCrossRefGoogle Scholar
[G+ 13] Ganter, N.. Power operations in orbifold Tate K-theory. Homol Homotopy Appl, 15(1):313–342, 2013. [322]CrossRefGoogle Scholar
Ganter, N.. Stringy power operations in Tate K-theory. ArXiv Mathematics e-prints, January 2007. [322]Google Scholar
Goerss, P. G. and Hopkins, M. J.. Moduli spaces of commutative ring spectra. In Structured ring spectra, pages 151–200. Cambridge University Press, Cambridge, 2004. [284, 309, 323, 326]Google Scholar
Ginzburg, V., Kapranov, M., and Vasserot, E.. Elliptic algebras and equivariant elliptic cohomology. arXiv preprint q-alg/9505012, 1995. [375]Google Scholar
Goerss, P., Lannes, J., and Morel, F.. Hopf algebras, Witt vectors, and Brown–Gitler spectra. In Algebraic topology (Oaxtepec, 1991), pages 111–128. American Mathematical Society, Providence, RI, 1993. [204, 205, 206, 209, 210, 211]10.1090/conm/146/01218CrossRefGoogle Scholar
Greenlees, J. P. C. and May, J. P.. Generalized Tate cohomology. American Mathematical Society, Providence, RI, 1995. [358]10.1090/memo/0543CrossRefGoogle Scholar
Goerss, P. G.. Hopf rings, Dieudonné modules, and E∗ Ω2 S3 . In Homotopy invariant algebraic structures (Baltimore, MD, 1998), pages 115–174. American Mathematical Society, Providence, RI, 1999. [174, 182, 185, 207, 208, 209]10.1090/conm/239/03600CrossRefGoogle Scholar
Goerss, P. G.. Quasi-coherent sheaves on the moduli stack of formal groups. Unpublished monograph, 2008. [27, 128]Google Scholar
Goerss, P. G.. Realizing families of Landweber exact homology theories. New topological contexts for Galois theory and algebraic geometry (BIRS 2008), 16:49–78, 2009. [372]10.2140/gtm.2009.16.49CrossRefGoogle Scholar
Goerss, P. G.. Topological modular forms [after Hopkins, Miller and Lurie]. Astérisque, (332):Exp. No. 1005, viii, 221–255, 2010. Séminaire Bourbaki. Volume 2008/2009. Exposés 997–1011. [323]Google Scholar
González, J.. A vanishing line in the BP〈1〉-adams spectral sequence. Topology, 39(6):1137–1153, 2000. [362]10.1016/S0040-9383(99)00002-6CrossRefGoogle Scholar
Giambalvo, V. and Pengelley, D. J.. The homology of MSpin. Math. Proc. Cambs. Philos. Soc., 95:427436, 1984. [353]Google Scholar
Grothendieck, A.. Revêtement étales et groupe fondamental (sga1). Lecture Notes in Math., 288, 1971. [56, 102]10.1007/BFb0069608CrossRefGoogle Scholar
Grothendieck, A.. Groupes de Barsotti-Tate et cristaux de Dieudonné. Les Presses de l’Université de Montréal, Montreal, Que., 1974. [196, 197, 200, 201, 214]Google Scholar
Gross, B. H.. On canonical and quasi-canonical liftings. Invent. Math., 84(2):321–326, 1986. [202]10.1007/BF01388810CrossRefGoogle Scholar
Grojnowski, I.. Delocalised equivariant elliptic cohomology. In Elliptic cohomology, pages 114–121. Cambridge University Press, Cambridge, 2007. [375]10.1017/CBO9780511721489.007CrossRefGoogle Scholar
Greenlees, J. P. C. and Sadofsky, H.. The Tate spectrum of vn-periodic complex oriented theories. Mathematische Zeitschrift, 222(3):391–405, 1996. [345]10.1007/BF02621873CrossRefGoogle Scholar
Greenlees, J. P. C. and Strickland, N. P.. Varieties and local cohomology for chromatic group cohomology rings. Topology, 38(5):1093–1139, 1999. [286, 359]10.1016/S0040-9383(98)00048-2CrossRefGoogle Scholar
Hartshorne, R.. Algebraic geometry. Springer-Verlag, New York, 1977. [54, 64, 65, 260]10.1007/978-1-4757-3849-0CrossRefGoogle Scholar
Harris, B.. Bott periodicity via simplicial spaces. J. Algebra, 62(2):450–454, 1980. [38]10.1016/0021-8693(80)90194-5CrossRefGoogle Scholar
Hopkins, M., Ando, M., and Strickland, N.. Elliptic cohomology of BO〈8〉 in positive characteristic. 1999. Unpublished. [270]Google Scholar
Hazewinkel, M.. Formal groups and applications. AMS Chelsea Publishing, Providence, RI, 2012. Corrected reprint of the 1978 original. [57, 122, 131]CrossRefGoogle Scholar
Dicke, R. H.. Dirac’s cosmology and Mach’s principle. Nature 192:440–441, 1990. [361]CrossRefGoogle Scholar
Hedayatzadeh, S. M. H.. Exterior powers of π-divisible modules over fields. J. Number Theory, 138:119–174, 2014. [218]10.1016/j.jnt.2013.10.023CrossRefGoogle Scholar
Hedayatzadeh, S. M. H.. Exterior powers of Lubin-Tate groups. J. Théor. Nombres Bordeaux, 27(1):77–148, 2015. [218]10.5802/jtnb.895CrossRefGoogle Scholar
Hopkins, M. J. and Gross, B. H.. Equivariant vector bundles on the Lubin–Tate moduli space. In Topology and representation theory (Evanston, IL, 1992), pages 23–88. American Mathematical Society, Providence, RI, 1994. [200, 202]CrossRefGoogle Scholar
Hopkins, M. J. and Gross, B. H.. The rigid analytic period mapping, Lubin–Tate space, and stable homotopy theory. Bull. Amer. Math. Soc. (N.S.), 30(1):76–86, 1994. [202]10.1090/S0273-0979-1994-00438-0CrossRefGoogle Scholar
Hopkins, M. J. and Hovey, M. A.. Spin cobordism determines real K-theory. Mathematische Zeitschrift, 210(1):181–196, 1992. [280, 354]10.1007/BF02571790CrossRefGoogle Scholar
Hopkins, M. J. and Hunton, J. R.. On the structure of spaces representing a Landweber exact cohomology theory. Topology, 34(1):29–36, 1995. [187, 209]10.1016/0040-9383(94)E0013-ACrossRefGoogle Scholar
Hill, M. A., Hopkins, M. J., and Ravenel, D. C.. On the nonexistence of elements of Kervaire invariant one. Ann. Math., 184(1):1–262, 2016. [164, 187, 375]10.4007/annals.2016.184.1.1CrossRefGoogle Scholar
Hida, H.. p-adic automorphic forms on Shimura varieties. Springer-Verlag, New York, 2004. [329]10.1007/978-1-4684-9390-0CrossRefGoogle Scholar
Hirzebruch, F.. Topological methods in algebraic geometry. Springer-Verlag, Berlin, 1995. Reprint of the 1978 edition. [273]Google Scholar
Hopkins, M. J., Kuhn, N. J., and Ravenel, D. C.. Generalized group characters and complex oriented cohomology theories. J. Amer. Math. Soc., 13(3):553–594, 2000. [78, 286, 287, 290, 294, 301, 306, 307, 359]10.1090/S0894-0347-00-00332-5CrossRefGoogle Scholar
Hopkins, M. J. and Lurie, J.. Ambidexterity in K (n)-local stable homotopy theory. www.math.harvard.edu/~lurie/papers/Ambidexterity.pdf, accessed: January 9, 2015. [211, 212, 215, 216, 217, 218, 221]Google Scholar
Hopkins, M. J. and Lawson, T.. Strictly commutative complex orientation theory. arXiv preprint arXiv:1603.00047, 2016. [319, 373]Google Scholar
Hughes, A., Lau, J. M., and Peterson, E.. Multiplicative 2-cocycles at the prime 2. J. Pure Appl. Algebra, 217(3):393–408, 2013. [356]10.1016/j.jpaa.2012.06.031CrossRefGoogle Scholar
Hahn, R. and Mitchell, S.. Iwasawa theory for K (1)-local spectra. Trans. Amer. Math. Soc., 359(11):5207–5238, 2007. [366]10.1090/S0002-9947-07-04204-3CrossRefGoogle Scholar
Hopkins, M. J. and Miller, H. R.. Elliptic curves and stable homotopy theory I. In Topological modular forms, pages 224–275. American Mathematical Society, Providence, RI, 2014. [323]Google Scholar
Hopkins, M. J., Mahowald, M., and Sadofsky, H.. Constructions of elements in Picard groups. In Topology and representation theory (Evanston, IL, 1992), pages 89–126. American Mathematical Society, Providence, RI, 1994. [160, 366]10.1090/conm/158/01454CrossRefGoogle Scholar
Hopkins, M. J.. Complex oriented cohomology theories and the language of stacks. Unpublished. [43, 106, 115, 127, 140, 144]Google Scholar
Hopkins, M. J.. Topological modular forms, the Witten genus, and the theorem of the cube. In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), pages 554–565. Birkhäuser, Basel, 1995. [279, 351, 361]10.1007/978-3-0348-9078-6_49CrossRefGoogle Scholar
Hopkins, M. J.. Algebraic topology and modular forms. In Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), pages 291–317. Higher Ed. Press, Beijing, 2002. [351]Google Scholar
Hopkins, M. J.. The mathematical work of Douglas C. Ravenel. Homol Homotopy Appl., 10(3):1–13, 2008. [xii, 361]10.4310/HHA.2008.v10.n3.a1CrossRefGoogle Scholar
Hopkins, M. J.. From spectra to stacks. In Topological modular forms, pages 118–126. American Mathematical Society, Providence, RI, 2014. [110, 147, 329]Google Scholar
Hopkins, M. J.. K (1)-local E∞ ring spectra. In Topological modular forms, pages 301–216. American Mathematical Society, Providence, RI, 2014. [331]Google Scholar
Hopkins, M. J.. The string orientation. In Topological modular forms, pages 127–142. American Mathematical Society, Providence, RI, 2014. [374]Google Scholar
Hovey, M.. Bousfield localization functors and Hopkins’ chromatic splitting conjecture. In The Čech centennial (Boston, MA, 1993), pages 225–250. American Mathematical Society, Providence, RI, 1995. [156, 363]Google Scholar
Hovey, M.. vn-elements in ring spectra and applications to bordism theory. Duke Math. J., 88(2):327–356, 1997. [354, 355]10.1215/S0012-7094-97-08813-XCrossRefGoogle Scholar
Hovey, M.. Morita theory for Hopf algebroids and presheaves of groupoids. Amer. J. Math., 124(6):1289–1318, 2002. [34, 101, 106]10.1353/ajm.2002.0033CrossRefGoogle Scholar
Hovey, M.. Homotopy theory of comodules over a Hopf algebroid. In Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic K-theory, pages 261–304. American Mathematical Society, Providence, RI, 2004. [107]Google Scholar
Hovey, M. and Sadofsky, H.. Tate cohomology lowers chromatic Bousfield classes. Proc. Amer. Math. Soc., 124(11):3579–3585, 1996. [345]10.1090/S0002-9939-96-03495-8CrossRefGoogle Scholar
Hopkins, M. J. and Smith, J. H.. Nilpotence and stable homotopy theory: II. Ann. Math. (2), 148(1):1–49, 1998. [148, 149, 150, 151, 152, 153, 159]10.2307/120991CrossRefGoogle Scholar
Hovey, M. and Strickland, N. P.. Morava K-theories and localisation. Mem. Amer. Math. Soc., 139(666):viii–100, 1999. [103, 144, 366]Google Scholar
Hovey, M., Shipley, B., and Smith, J.. Symmetric spectra. J. Amer. Math. Soc., 13(1):149–208, 2000. [74]10.1090/S0894-0347-99-00320-3CrossRefGoogle Scholar
Hunton, J. R. and Turner, P. R.. Coalgebraic algebra. J. Pure Appl. Algebra, 129(3):297–313, 1998. [207]10.1016/S0022-4049(97)00076-5CrossRefGoogle Scholar
Huan, Z.. Quasi-elliptic cohomology and its power operations. arXiv preprint arXiv:1612.00930, 2016. [322]Google Scholar
Huber, A.. On the Parshin–Beilinson adeles for schemes. In Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, volume 61, page 249. Springer, New York, 1991. [164]Google Scholar
Husemöller, D.. Elliptic curves. Springer-Verlag, New York, second edition, 2004. [259]Google Scholar
Johnson, N. and Noel, J.. For complex orientations preserving power operations, p-typicality is atypical. Topology Appl., 157(14):2271– 2288, 2010. [77, 131]10.1016/j.topol.2010.06.007CrossRefGoogle Scholar
Johnson, D. C. and Wilson, W. S.. Projective dimension and Brown– Peterson homology. Topology, 12:327–353, 1973. [193]10.1016/0040-9383(73)90027-XCrossRefGoogle Scholar
Johnson, D. C. and Wilson, W. S.. BP operations and Morava’s extraordinary K-theories. Math. Z., 144(1):55–75, 1975. [149]10.1007/BF01214408CrossRefGoogle Scholar
Katz, N. M.. Crystalline cohomology, Dieudonné modules, and Jacobi sums. In Automorphic forms, representation theory and arithmetic (Bombay, 1979), pages 165–246. Tata Institute of Fundamental Research, Bombay, 1981. [195, 196, 197, 200]10.1007/978-3-662-00734-1_6CrossRefGoogle Scholar
Kitaev, A.. Periodic table for topological insulators and superconductors. In AIP conference proceedings, volume 1134, pages 22–30. American Institute of Physics, College Park, MD, 2009. [377]10.1063/1.3149495CrossRefGoogle Scholar
Kitchloo, N. and Laures, G.. Real structures and Morava K-theories. K-Theory, 25(3):201–214, 2002. [281]10.1023/A:1015683917463CrossRefGoogle Scholar
Kitchloo, N., Laures, G., and Wilson, W. S.. The Morava K-theory of spaces related to BO. Adv. Math., 189(1):192–236, 2004. [147, 280]10.1016/j.aim.2003.10.008CrossRefGoogle Scholar
Katz, N. M. and Mazur, B.. Arithmetic moduli of elliptic curves. Princeton University Press, Princeton, NJ, 1985. [270]10.1515/9781400881710CrossRefGoogle Scholar
Knight, E.. A p-adic Jacquet–Langlands correspondence. PhD thesis, Harvard University Cambridge, MA, 2016. [367]Google Scholar
Kochman, S. O.. A chain functor for bordism. Trans. Amer. Math. Soc., 239:167–196, 1978. [1]CrossRefGoogle Scholar
Krause, H.. Smashing subcategories and the telescope conjecture: an algebraic approach. Invent. Math., 139(1):99–133, 2000. [359]10.1007/s002229900022CrossRefGoogle Scholar
Kříž, I.. All complex Thom spectra are harmonic. In Topology and representation theory (Evanston, IL, 1992), pages 127–134. American Mathematical Society, Providence, RI, 1994. [158, 306]10.1090/conm/158/01455CrossRefGoogle Scholar
Kreck, M. and Stolz, S.. H2 -bundles and elliptic homology. Acta Mathematica, 171(2):231–261, 1993. [355]10.1007/BF02392533CrossRefGoogle Scholar
Kuhn, N. J.. Character rings in algebraic topology. In Advances in homotopy theory (Cortona, 1988), pages 111–126. Cambridge University Press, Cambridge, 1989. [299]10.1017/CBO9780511662614.012CrossRefGoogle Scholar
Kuhn, N. J.. A guide to telescopic functors. Homol Homotopy Appl., 10(3):291–319, 2008. [339]10.4310/HHA.2008.v10.n3.a13CrossRefGoogle Scholar
Landweber, P. S.. Invariant regular ideals in Brown–Peterson homology. Duke Math. J., 42(3):499–505, 1975. [130]10.1215/S0012-7094-75-04247-7CrossRefGoogle Scholar
Landweber, P. S.. Homological properties of comodules over MU∗ (MU) and BP∗ (BP). Amer. J. Math., 98(3):591–610, 1976. [140]10.2307/2373808CrossRefGoogle Scholar
Landweber, P. S.. Elliptic cohomology and modular forms. In Elliptic curves and modular forms in algebraic topology, pages 55–68. Springer, New York, 1988. [354]10.1007/BFb0078038CrossRefGoogle Scholar
Laures, G.. An E∞ splitting of spin bordism. Amer. J. Math., 125(5):977–1027, 2003. [280]10.1353/ajm.2003.0032CrossRefGoogle Scholar
Laures, G.. K (1)-local topological modular forms. Invent. Math., 157(2):371–403, 2004. [331]10.1007/s00222-003-0355-yCrossRefGoogle Scholar
Lawson, T.. Realizability of the Adams–Novikov spectral sequence for formal A-modules. Proc. Amer. Math. Soc., 135(3):883–890, 2007. [373, 376]10.1090/S0002-9939-06-08521-2CrossRefGoogle Scholar
Lawson, T.. An overview of abelian varieties in homotopy theory. In New topological contexts for Galois theory and algebraic geometry (BIRS 2008), pages 179–214. Geometry and Topology Publishers, Coventry, 2009. [331]10.2140/gtm.2009.16.179CrossRefGoogle Scholar
Lawson, T.. Structured ring spectra and displays. Geom. Topol., 14(2):1111–1127, 2010. [203]10.2140/gt.2010.14.1111CrossRefGoogle Scholar
Lawson, T.. Secondary power operations and the Brown–Peterson spectrum at the prime 2. arXiv preprint arXiv:1703.00935, 2017. [131, 373]10.4007/annals.2018.188.2.3CrossRefGoogle Scholar
Lazard, M.. Sur les groupes de Lie formels à un paramètre. Bull. Soc. Math. France, 83:251–274, 1955. [111, 115, 132]10.24033/bsmf.1462CrossRefGoogle Scholar
Lazard, M.. Commutative formal groups. Springer-Verlag, Berlin, 1975. [55, 131, 204, 369, 370, 371, 372]10.1007/BFb0070554CrossRefGoogle Scholar
Lazarev, A.. Deformations of formal groups and stable homotopy theory. Topology, 36(6):1317–1331, 1997. [136, 137, 216]10.1016/S0040-9383(96)00051-1CrossRefGoogle Scholar
Lin, W. H.. On conjectures of Mahowald, Segal and Sullivan. Math. Proc. Cambridge Philos. Soc., 87(3):449–458, 1980. [357]10.1017/S0305004100056887CrossRefGoogle Scholar
Lawson, T. and Naumann, N.. Commutativity conditions for truncated Brown–Peterson spectra of height 2. J. Topol., 5(1):137–168, 2012. [131, 194]10.1112/jtopol/jtr030CrossRefGoogle Scholar
Landweber, P. S., Ravenel, D. C., and Stong, R. E.. Periodic cohomology theories defined by elliptic curves. Contemp. Math., 181:317–317, 1995. [4, 354]10.1090/conm/181/02040CrossRefGoogle Scholar
Laures, G. and Schuster, B.. Towards a splitting of the K (2)-local string bordism spectrum. ArXiv e-prints, October 2017. [275, 353]Google Scholar
Lubin, J. and Tate, J.. Formal complex multiplication in local fields. Ann. Math. (2), 81(2): 380–387, 1965. [202]10.2307/1970622CrossRefGoogle Scholar
Lubin, J. and Tate, J.. Formal moduli for one-parameter formal Lie groups. Bull. Soc. Math. France, 94:49–59, 1966. [134, 136, 138]10.24033/bsmf.1633CrossRefGoogle Scholar
Lubin, J.. Finite subgroups and isogenies of one-parameter formal lie groups. Ann. Math., 85(2):296–302, 1967. [316]10.2307/1970443CrossRefGoogle Scholar
Lurie, J.. Chromatic homotopy. www.math.harvard.edu/~lurie/252x.html, accessed: September 22, 2016. [26, 73, 119, 124, 130, 138, 140, 157]Google Scholar
Lurie, J.. Elliptic cohomology II: orientations. http://math.harvard.edu/∼lurie/papers/Elliptic-II.pdf, accessed: February 4, 2018. [361]Google Scholar
Lurie, J.. Higher algebra. www.math.harvard.edu/~lurie/papers/HA.pdf, accessed: September 22, 2016. [74, 77, 79, 103, 110, 167, 283]Google Scholar
Lurie, J.. Spectral algebraic geometry. www.math.harvard.edu/~lurie/papers/SAG-rootfile.pdf, accessed: September 22, 2016. [80, 104]Google Scholar
Lurie, J.. A survey of elliptic cohomology. www.math.harvard.edu/∼lurie/papers/survey.pdf, accessed: April 4, 2017. [263, 323, 375, 376]Google Scholar
Lurie, J.. Higher topos theory. Princeton University Press, Princeton, NJ, 2009. [323]10.1515/9781400830558CrossRefGoogle Scholar
Mahowald, M.. Ring spectra which are Thom complexes. Duke Math. J., 46(3):549–559, 1979. [13]10.1215/S0012-7094-79-04628-3CrossRefGoogle Scholar
Manin, Yu I. The theory of commutative formal groups over fields of finite characteristic. Russ. Math. Surv., 18(6):1, 1963. [325]10.1070/RM1963v018n06ABEH001142CrossRefGoogle Scholar
Mandell, M. A.. E∞ algebras and p-adic homotopy theory. Topology, 40(1):43–94, 2001. [308]10.1016/S0040-9383(99)00053-1CrossRefGoogle Scholar
Margolis, H. R.. Spectra and the Steenrod algebra. North-Holland Publishing Co., Amsterdam, 1983. [155]Google Scholar
Matsumura, H.. Commutative ring theory. Cambridge University Press, Cambridge, second edition, 1989. Translated from the Japanese by M. Reid. [145]Google Scholar
Mathew, A.. The Galois group of a stable homotopy theory. Adv. Math., 291:403–541, 2016. [104]10.1016/j.aim.2015.12.017CrossRefGoogle Scholar
May, J. P.. Problems in infinite loop space theory. In Notas de Matemfiticas y Simposio, Ntimero, volume 1, pages 111–125, 1974. [373]Google Scholar
May, J. P.. Classifying spaces and fibrations. Mem. Amer. Math. Soc., 1(155):xiii–98, 1975. [11]Google Scholar
May, J. P.. E∞ ring spaces and E∞ ring spectra. Springer-Verlag, Berlin, 1977. [16, 284, 334]10.1007/BFb0097608CrossRefGoogle Scholar
May, J. P.. Equivariant homotopy and cohomology theory. American Mathematical Society, Providence, RI, 1996. [77, 79, 288]10.1090/cbms/091CrossRefGoogle Scholar
May, J. P.. A concise course in algebraic topology. University of Chicago Press, Chicago, IL, 1999. [248]Google Scholar
McClure, J. E.. Dyer–Lashof operations in K-theory. Bull. Amer. Math. Soc. (N.S.), 8(1):67–72, 1983. [327]10.1090/S0273-0979-1983-15086-3CrossRefGoogle Scholar
McTague, C.. tmf is not a ring spectrum quotient of String bordism. arXiv preprint arXiv:1312.2440, 2013. [355]Google Scholar
Messing, W.. The crystals associated to Barsotti–Tate groups: with applications to abelian schemes. Springer-Verlag, Berlin, 1972. [196]10.1007/BFb0058301CrossRefGoogle Scholar
Michaelis, W.. Coassociative coalgebras. In Handbook of algebra, volume 3, pages 587–788. North-Holland Publishing Co., Amsterdam, 2003. [221, 222]Google Scholar
Miller, H.. Notes on Cobordism. www-math.mit.edu/~hrm/papers/cobordism.pdf, accessed: October 4, 2016. [127]Google Scholar
Miller, H.. Sheaves, gradings, and the exact functor theorem. Unpublished. [102]Google Scholar
Milnor, J.. The Steenrod algebra and its dual. Ann. Math. (2), 67:150–171, 1958. [26]10.2307/1969932CrossRefGoogle Scholar
Miller, H. R.. On relations between Adams spectral sequences, with an application to the stable homotopy of a Moore space. J. Pure Appl. Algebra, 20(3):287–312, 1981. [110]10.1016/0022-4049(81)90064-5CrossRefGoogle Scholar
Miller, H. R.. Universal Bernoulli numbers and the S 1 -transfer. In Current trends in algebraic topology, Part 2 (London, Ont., 1981), pages 437–449. American Mathematical Society, Providence, RI, 1982. [348, 374]Google Scholar
Milne, J. S.. Abelian varieties. 2008. www.jmilne.org/math/CourseNotes/av.html, accessed July 20, 2018. [260, 261, 325]Google Scholar
Mitchell, S. A.. Power series methods in unoriented cobordism. In Proceedings of the Northwestern Homotopy Theory Conference (Evanston, Ill., 1982), pages 247–254. American Mathematical Society, Providence, RI, 1983. [45]10.1090/conm/019/711056CrossRefGoogle Scholar
Mitchell, S. A.. K (1)-local homotopy theory, Iwasawa theory, and algebraic K-theory. In Handbook of K-theory. Springer Science & Business Media, New York, 2005. [157, 366]Google Scholar
Milnor, J. W. and Moore, J. C.. On the structure of Hopf algebras. Ann. Math. (2), 81:211–264, 1965. [38, 255]10.2307/1970615CrossRefGoogle Scholar
Mazur, B. and Messing, W.. Universal extensions and one dimensional crystalline cohomology. Springer-Verlag, Berlin, 1974. [200, 201, 369]10.1007/BFb0061628CrossRefGoogle Scholar
Mathew, A. and Meier, L.. Affineness and chromatic homotopy theory. J. Topol., 8(2):476–528, 2015. [362]10.1112/jtopol/jtv005CrossRefGoogle Scholar
Mathew, A., Naumann, N., and Noel, J.. On a nilpotence conjecture of j. p. may J. P. May. J. Topol., 8(4):917–932, 2015. [156]10.1112/jtopol/jtv021CrossRefGoogle Scholar
Morava, J.. Noetherian localisations of categories of cobordism comodules. Ann. Math. (2), 121(1):1–39, 1985. [201, 202, 364]10.2307/1971192CrossRefGoogle Scholar
Morava, J.. Forms of K-theory. Math. Z., 201(3):401–428, 1989. [ix, 4, 198, 266, 267]10.1007/BF01214905CrossRefGoogle Scholar
Morava, J.. The motivic Thom isomorphism. In Elliptic cohomology, pages 265–285. Cambridge University Press, Cambridge, 2007. [270]10.1017/CBO9780511721489.014CrossRefGoogle Scholar
Morava, J.. Abelian varieties and the Kervaire invariant. arXiv preprint arXiv:1105.0539, 2011. [164]Google Scholar
Morava, J.. Local fields and extraordinary K-theory. arXiv preprint arXiv:1207.4011, 2012. [286]Google Scholar
Morava, J.. Complex orientations for T HH of some perfectoid fields. arXiv, 2016. [270, 361]Google Scholar
Mahowald, M. E. and Ravenel, D. C.. The root invariant in homotopy theory. Topology, 32(4):865–898, 1993. [358]10.1016/0040-9383(93)90055-ZCrossRefGoogle Scholar
Mahowald, M., Ravenel, D., and Shick, P.. The triple loop space approach to the telescope conjecture. In Homotopy methods in algebraic topology (Boulder, CO, 1999), pages 217–284. American Mathematical Society, Providence, RI, 2001. [359]10.1090/conm/271/04358CrossRefGoogle Scholar
Miller, H. R., Ravenel, D. C., and Wilson, W. S.. Periodic phenomena in the Adams–Novikov spectral sequence. Ann. Math. (2), 106(3):469–516, 1977. [108, 163, 164, 362]10.2307/1971064CrossRefGoogle Scholar
Mahowald, M. and Shick, P.. Root invariants and periodicity in stable homotopy theory. Bull. Lond. Math. Soc., 20(3):262–266, 1988. [358]10.1112/blms/20.3.262CrossRefGoogle Scholar
Mahowald, M. and Sadofsky, H.. vn telescopes and the Adams spectral sequence. Duke Math. J., 78(1):101–129, 1995. [359]10.1215/S0012-7094-95-07806-5CrossRefGoogle Scholar
Mazur, B. and Swinnerton-Dyer, P.. Arithmetic of Weil curves. Invent. Math., 25(1):1–61, 1974. [345]10.1007/BF01389997CrossRefGoogle Scholar
Mosher, R. E. and Tangora, M. C.. Cohomology operations and applications in homotopy theory. Harper & Row, New York, 1968. [26, 32]Google Scholar
Mahowald, M. and Thompson, R. D.. The K-theory localization of an unstable sphere. Topology, 31(1):133–141, 1992. [309]10.1016/0040-9383(92)90066-QCrossRefGoogle Scholar
Mumford, D.. On the equations defining abelian varieties: I. Invent. Math., 1:287–354, 1966. [261]10.1007/BF01389737CrossRefGoogle Scholar
Mumford, D.. On the equations defining abelian varieties: II. Invent. Math., 3:75–135, 1967. [261]10.1007/BF01389741CrossRefGoogle Scholar
Mumford, D.. On the equations defining abelian varieties: III. Invent. Math., 3:215–244, 1967. [261]10.1007/BF01425401CrossRefGoogle Scholar
Naumann, N.. The stack of formal groups in stable homotopy theory. Adv. Math., 215(2):569–600, 2007. [107]10.1016/j.aim.2007.04.007CrossRefGoogle Scholar
Nave, L. S.. The Smith–Toda complex V ((p + 1)/2) does not exist. Ann. Math. (2), 171(1):491–509, 2010. [148]10.4007/annals.2010.171.491CrossRefGoogle Scholar
Nishida, G.. The nilpotency of elements of the stable homotopy groups of spheres. J. Math. Soc. Japan, 25:707–732, 1973. [148]10.2969/jmsj/02540707CrossRefGoogle Scholar
Ochanine, S.. Modules de SU-bordisme: applications. Bull. Soc. Math. Fr, 115:257–289, 1987. [354]10.24033/bsmf.2078CrossRefGoogle Scholar
Ochanine, S.. Sur les genres multiplicatifs définis par des intégrales elliptiques. Topology, 26(2):143–151, 1987. [3]10.1016/0040-9383(87)90055-3CrossRefGoogle Scholar
Ochanine, S.. Elliptic genera, modular forms over KO∗ , and the Brown–Kervaire invariant. Math. Z., 206(1):277–291, 1991. [3]10.1007/BF02571343CrossRefGoogle Scholar
Pengelley, D. J.. The homotopy type of MSU. Amer. J. Math., 104(5):1101–1123, 1982. [353]10.2307/2374085CrossRefGoogle Scholar
Polishchuk, A.. Abelian varieties, theta functions and the Fourier transform. Cambridge University Press, Cambridge, 2003. [261]10.1017/CBO9780511546532CrossRefGoogle Scholar
Priddy, S.. A cellular construction of BP and other irreducible spectra. Math. Z., 173(1):29–34, 1980. [360]10.1007/BF01215522CrossRefGoogle Scholar
Peterson, E. and Stapleton, N.. Isogenies of formal groups laws and power operations in the cohomology theories En , revisited. In preparation. [320]Google Scholar
Quillen, D.. On the formal group laws of unoriented and complex cobordism theory. Bull. Amer. Math. Soc., 75:1293–1298, 1969. [73]10.1090/S0002-9904-1969-12401-8CrossRefGoogle Scholar
Quillen, D.. Elementary proofs of some results of cobordism theory using Steenrod operations. Adv. Math., 7:29–56, 1971. [82, 83, 90, 91, 92, 94]10.1016/0001-8708(71)90041-7CrossRefGoogle Scholar
Ravenel, D. C.. The cohomology of the Morava stabilizer algebras. Math. Z., 152(3):287–297, 1977. [364]10.1007/BF01488970CrossRefGoogle Scholar
Ravenel, D. C.. The non-existence of odd primary Arf invariant elements in stable homotopy. Math. Proc. Camb. Phil. Soc. 83:429– 443, 1978. [164, 349, 350, 376]10.1017/S0305004100054712CrossRefGoogle Scholar
Ravenel, D. C.. A novice’s guide to the Adams–Novikov spectral sequence. In Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II, pages 404–475. Springer, Berlin, 1978. [41, 108]Google Scholar
Ravenel, D. C.. Localization with respect to certain periodic homology theories. Amer. J. Math., 106(2):351–414, 1984. [104, 147, 148, 149, 151, 359]10.2307/2374308CrossRefGoogle Scholar
Ravenel, D. C.. Complex cobordism and stable homotopy groups of spheres. Academic Press, Orlando, FL, 1986. [x, 32, 33, 36, 106, 109, 127, 163]Google Scholar
Ravenel, D. C.. Nilpotence and periodicity in stable homotopy theory. Princeton University Press, Princeton, NJ, 1992. [156, 158]Google Scholar
Ravenel, D. C.. Life after the telescope conjecture. In Algebraic K-theory and algebraic topology (Lake Louise, AB, 1991), pages 205–222. Kluwer Academic Publishers, Dordrecht, 1993. [359]10.1007/978-94-017-0695-7_10CrossRefGoogle Scholar
Rezk, C.. Elliptic cohomology and elliptic curves (Felix Klein lectures, Bonn 2015). www.math.uiuc.edu/~rezk/felix-klein-lectures-notes.pdf, accessed: October 7, 2016. [133, 269]Google Scholar
Rezk, C.. Notes on the Hopkins–Miller theorem. www.math.uiuc.edu/∼rezk/hopkins-miller-thm.pdf, accessed: October 10, 2016. [134]Google Scholar
Rezk, C.. Supplementary notes for Math 512. www.math.uiuc.edu/∼rezk/512-spr2001-notes.pdf, accessed: October 28, 2016. [161, 162, 329]Google Scholar
Rezk, C.. The units of a ring spectrum and a logarithmic cohomology operation. J. Amer. Math. Soc., 19(4):969–1014, 2006. [339, 340, 348]10.1090/S0894-0347-06-00521-2CrossRefGoogle Scholar
Rezk, C.. Rings of power operations for Morava E-theories are Koszul. ArXiv e-prints, April 2012. [313]Google Scholar
Rudyak, Y. B.. On Thom spectra, orientability, and cobordism. Springer-Verlag, Berlin, 1998. [12, 76, 89, 90]Google Scholar
Ravenel, D. C. and Wilson, W. S.. The Morava K-theories of Eilenberg–Mac Lane spaces and the Conner–Floyd conjecture. Amer. J. Math., 102(4):691–748, 1980. [172, 174, 180, 211, 212, 213, 216, 218]10.2307/2374093CrossRefGoogle Scholar
Ravenel, D. C. and Wilson, W. S.. The Hopf ring for complex cobordism. J. Pure Appl. Algebra, 9(3):241–280, 1976/1977. [181, 183, 188, 189, 191, 192, 194]10.1016/0022-4049(77)90070-6CrossRefGoogle Scholar
Ravenel, D. C., Wilson, W. S., and Yagita, N.. Brown–Peterson cohomology from Morava K-theory. K-Theory, 15(2):147–199, 1998. [218]10.1023/A:1007776725714CrossRefGoogle Scholar
Sadofsky, H.. Hopkins’ and Mahowald’s picture of Shimomura’s v1 -Bockstein spectral sequence calculation. In Algebraic topology (Oaxtepec, 1991), pages 407–418. American Mathematical Society, Providence, RI, 1993. [365]10.1090/conm/146/01236CrossRefGoogle Scholar
Salch, A.. The cohomology of the height four Morava stabilizer group at large primes. arXiv preprint arXiv:1607.01108, 2016. [376]Google Scholar
Schoeller, C.. Étude de la catégorie des algèbres de Hopf commutatives connexes sur un corps. Manuscripta Math., 3:133–155, 1970. [204, 205, 206]10.1007/BF01273307CrossRefGoogle Scholar
Segal, G.. Cohomology of topological groups. In Symposia Mathematica, Vol. IV (INDAM, Rome, 1968/69), pages 377–387. Academic Press, London, 1970. [172]Google Scholar
Segal, G.. Elliptic cohomology [after Landweberstong, Ochanine, Witten, and others]. Astérisque, 161–162:187–201, 1988. [377]Google Scholar
Senger, A.. The Brown–Peterson spectrum is not E2(p 2 +2) at odd primes. ArXiv e-prints, October 2017. [373]Google Scholar
Brian Shay, P.. mod p Wu formulas for the Steenrod algebra and the Dyer–Lashof algebra. Proc. Amer. Math. Soc., 63(2):339–347, 1977. [249]Google Scholar
Shimomura, K.. On the Adams–Novikov spectral sequence and products of β-elements. Hiroshima Math. J., 16(1):209–224, 1986. [366]Google Scholar
Silverman, J. H.. The arithmetic of elliptic curves. Springer-Verlag, New York, 1986. [325]10.1007/978-1-4757-1920-8CrossRefGoogle Scholar
Silverman, J. H.. Advanced topics in the arithmetic of elliptic curves. Springer-Verlag, New York, 1994. [266]10.1007/978-1-4612-0851-8CrossRefGoogle Scholar
Singer, W. M.. Connective fiberings over BU and U. Topology, 7:271–303, 1968. [4, 249]10.1016/0040-9383(68)90006-2CrossRefGoogle Scholar
Sprang, J. and Naumann, N.. p-adic interpolation and multiplicative orientations of KO and tmf (with an appendix by Niko Naumann). ArXiv e-prints, September 2014. [374]Google Scholar
Schlank, T. M. and Stapleton, N.. A transchromatic proof of Strickland’s theorem. Adv. Math., 285:1415–1447, 2015. [310, 311, 312]10.1016/j.aim.2015.07.025CrossRefGoogle Scholar
Stolz, S. and Teichner, P.. What is an elliptic object? London Math. Soc. Lecture Note Ser., 308:247, 2004. [377]Google Scholar
Stolz, S. and Teichner, P.. Supersymmetric field theories and generalized cohomology. In Mathematical foundations of quantum field theory and perturbative string theory, pages 279–340. American Mathematical Society, Providence, RI, 2011. [377]10.1090/pspum/083/2742432CrossRefGoogle Scholar
Stapleton, N.. Transchromatic generalized character maps. Algebr. Geom. Topol., 13(1):171–203, 2013. [286, 359]10.2140/agt.2013.13.171CrossRefGoogle Scholar
The Stacks Project Authors. Stacks Project. http://stacks.math.columbia.edu, accessed July 20, 2018, 2014. [101]Google Scholar
Stapleton, N.. Transchromatic twisted character maps. J. Homotopy Relat Struct, 10(1):29–61, 2015. [359]10.1007/s40062-013-0040-9CrossRefGoogle Scholar
Steenrod, N. E.. Cyclic reduced powers of cohomology classes. PNAS, 39(3):217–223, 1953. [83]10.1073/pnas.39.3.217CrossRefGoogle ScholarPubMed
Steenrod, N. E.. Homology groups of symmetric groups and reduced power operations. PNAS, 39(3):213–217, 1953. [83]10.1073/pnas.39.3.213CrossRefGoogle ScholarPubMed
Stong, R. E.. Determination of H∗ (BO(k, · · · , ∞), Z2 ) and H ∗ (BU(k, · · · , ∞), Z2). Trans. Amer. Math. Soc., 107:526–544, 1963. [4, 249]Google Scholar
Stojanoska, V.. Duality for topological modular forms. Doc. Math., 17:271–311, 2012. [331]10.4171/dm/368CrossRefGoogle Scholar
Strickland, N. P.. Formal schemes for K-theory spaces. Unpublished. [270, 280]Google Scholar
Strickland, N. P.. Functorial philosophy for formal phenomena. http://hopf.math.purdue.edu/Strickland/fpfp.pdf, accessed: January 9, 2014. [6, 23, 51, 65, 72, 160, 198, 202, 204, 275, 312, 359]Google Scholar
Strickland, N. P.. On the p-adic interpolation of stable homotopy groups. In Adams Memorial Symposium on Algebraic Topology, 2 (Manchester, 1990), pages 45–54. Cambridge University Press, Cambridge, 1992. [366]10.1017/CBO9780511526312.010CrossRefGoogle Scholar
Strickland, N. P.. Finite subgroups of formal groups. J. Pure Appl. Algebra, 121(2):161–208, 1997. [133, 311, 312, 313, 315, 316]10.1016/S0022-4049(96)00113-2CrossRefGoogle Scholar
Strickland, N. P.. Morava E-theory of symmetric groups. Topology, 37(4):757–779, 1998. [311, 312, 313]10.1016/S0040-9383(97)00054-2CrossRefGoogle Scholar
Strickland, N. P.. Products on MU-modules. Trans. Amer. Math. Soc., 351(7):2569–2606, 1999. [131, 147, 194]10.1090/S0002-9947-99-02436-8CrossRefGoogle Scholar
Strickland, N. P.. Formal schemes and formal groups. In Homotopy invariant algebraic structures (Baltimore, MD, 1998), pages 263– 352. American Mathematical Society, Providence, RI, 1999. [x, 20, 23, 34, 52, 54, 56, 61, 65, 70, 72, 181, 187, 222, 223, 224, 225, 314, 359]Google Scholar
Strickland, N. P.. Gross–Hopkins duality. Topology, 39(5):1021– 1033, 2000. [159]10.1016/S0040-9383(99)00049-XCrossRefGoogle Scholar
Strickland, N. P.. Formal groups. https://neil-strickland.staff.shef.ac.uk/courses/formalgroups/fg.pdf, accessed July 20, 2018, 2006. [44, 45, 130, 132, 133]Google Scholar
Stroilova, O.. The generalized Tate construction. PhD thesis, Massachusetts Institute of Technology, 2012. [358]Google Scholar
Schwänzl, R., Vogt, R. M., and Waldhausen, F.. Adjoining roots of unity to E∞ ring spectra in good cases: a remark. Contemp. Math, 239:245–249, 1999. [372]10.1090/conm/239/03606CrossRefGoogle Scholar
Switzer, R. M.. Algebraic topology: homotopy and homology. Springer-Verlag, Berlin, 2002. Reprint of the 1975 original [Springer, New York]. [12, 42, 69, 71, 176, 353]Google Scholar
Shimomura, K. and Yabe, A.. On the chromatic E1 –term . In Topology and representation theory (Evanston, IL, 1992), pages 217–228. American Mathematical Society, Providence, RI, 1994. [366]10.1090/conm/158/01461CrossRefGoogle Scholar
Shimomura, K. and Yabe, A.. The homotopy groups π∗ (L2 S 0 ). Topology, 34(2):261–289, 1995. [366]10.1016/0040-9383(94)00032-GCrossRefGoogle Scholar
Takhtajan, L. A.. Quantum mechanics for mathematicians. American Mathematical Society, Providence, RI, 2008. [376]10.1090/gsm/095CrossRefGoogle Scholar
Tate, J.. The work of David Mumford. In Fields medallists’ lectures, pages 219–223. World Scientific, Singapore, 1997. [261]10.1142/9789812385215_0030CrossRefGoogle Scholar
Thompson, R.. An unstable change of rings for Morava E-theory. ArXiv e-prints, September 2014. [313]Google Scholar
Torii, T.. On degeneration of one-dimensional formal group laws and applications to stable homotopy theory. Amer. J. Math., 125(5):1037–1077, 2003. [364]10.1353/ajm.2003.0036CrossRefGoogle Scholar
Torii, T.. Milnor operations and the generalized Chern character. In Proceedings of the Nishida Fest (Kinosaki 2003), pages 383–421. Geometry and Topology Publishers, Coventry, 2007. [364]Google Scholar
Torii, T.. Comparison of Morava E-theories. Math. Z., 266(4):933– 951, 2010. [364]10.1007/s00209-009-0605-9CrossRefGoogle Scholar
Torii, T.. HKR characters, p-divisible groups and the generalized Chern character. Trans. Amer. Math. Soc., 362(11):6159–6181, 2010. [364]10.1090/S0002-9947-2010-05194-3CrossRefGoogle Scholar
Torii, T.. K (n)-localization of the K (n + 1)-local En+1 -Adams spectral sequences. Pacific J. Math., 250(2):439–471, 2011. [364]10.2140/pjm.2011.250.439CrossRefGoogle Scholar
Thomason, R. W. and Wilson, W. S.. Hopf rings in the bar spectral sequence. Quart. J. Math. Oxford Ser. (2), 31(124):507–511, 1980. [172]10.1093/qmath/31.4.507CrossRefGoogle Scholar
Vakil, R.. The rising sea: foundations of algebraic geometry. 2015. Preprint. http://math.stanford.edu/~vakil/216blog, accessed January 15, 2013. [64]Google Scholar
Vistoli, A.. Grothendieck topologies, fibered categories and descent theory. In Fundamental algebraic geometry, pages 1–104. American Mathematical Society, Providence, RI, 2005. [102]Google Scholar
Wang, G.. Unstable chromatic homotopy theory. PhD thesis, Massachusetts Institute of Technology, 2015. [362]Google Scholar
Weil, A.. Sur certains groupes d’opérateurs unitaires. Acta Mathematica, 111(1):143–211, 1964. [260]10.1007/BF02391012CrossRefGoogle Scholar
Weil, A.. Basic number theory. Springer-Verlag, New York, third edition, 1974. [361]10.1007/978-3-642-61945-8CrossRefGoogle Scholar
Weinstein, J.. The geometry of Lubin–Tate spaces. http://math.bu.edu/people/jsweinst/FRGLecture.pdf, accessed July 20, 2018, 2011. [195]Google Scholar
Wilson, W. S.. The Ω-spectrum for Brown–Peterson cohomology: I. Comment. Math. Helv., 48:45–55, 1973; corrigendum, ibid. 194. [194]10.1007/BF02566110CrossRefGoogle Scholar
Wilson, W. S.. The Ω-spectrum for Brown–Peterson cohomology: II. Amer. J. Math., 97:101–123, 1975. [194]10.2307/2373662CrossRefGoogle Scholar
Wilson, W. S.. Brown–Peterson homology: an introduction and sampler. Conference Board of the Mathematical Sciences, Washington, DC, 1982. [129, 130, 164, 174, 175, 183, 189, 193]10.1090/cbms/048CrossRefGoogle Scholar
Witten, E.. Elliptic genera and quantum field theory. Comm. Math. Phys., 109(4):525–536, 1987. [3]10.1007/BF01208956CrossRefGoogle Scholar
Witten, E.. The index of the Dirac operator in loop space. In Elliptic curves and modular forms in algebraic topology (Princeton, NJ, 1986), pages 161–181. Springer, Berlin, 1988. [3]10.1007/BFb0078045CrossRefGoogle Scholar
Yagita, N.. On the Steenrod algebra of Morava K-theory. J. London Math. Soc. (2), 22(3):423–438, 1980. [280]10.1112/jlms/s2-22.3.423CrossRefGoogle Scholar
Yu, J.-Kang. On the moduli of quasi-canonical liftings. Compositio Math., 96(3):293–321, 1995. [202]Google Scholar
Zhu, Y.. Norm coherence for descent of level structures on formal deformations. ArXiv e-prints, June 2017. [320]Google Scholar
Zink, T.. Cartiertheorie kommutativer formaler Gruppen. BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1984. [135, 201, 369]Google Scholar
Zink, T.. The display of a formal p-divisible group. Astérisque, (278):127–248, 2002. [203]Google Scholar
Accessibility standard: Unknown
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
Accessibility compliance for the PDF of this chapter is currently unknown
and may be updated in the future.