Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-02T08:14:29.548Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  01 December 2022

Joachim Schwermer
Joachim Schwermer
Affiliation:
Universität Wien, Austria
Get access

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.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Reduction Theory and Arithmetic Groups , pp. 350 - 356
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

An, J. and Wang, Z. (2008). Nonabelian cohomology with coefficients in Lie groups. Trans. Amer. Math. Soc., 360:3019–3040.Google Scholar
Artin, E. and Tate, J. (1968). Class Field Theory. W. A. Benjamin, New York–Amsterdam.Google Scholar
Ash, A. and Borel, A. (1990). Generalized modular symbols. In Cohomology of Arithmetic Groups and Automorphic Forms (Luminy-Marseille, 1989), Lect. Notes in Maths., volume 1447, pages 57–75. Springer, Berlin.Google Scholar
Ash, A. and Ginzburg, D. (1996). Generalized modular symbols and relative Lie algebra cohomology. Pacific J. Math., 175:337–355.Google Scholar
Atiyah, M. F. and MacDonald, I. G. (1969). Introduction to Commutative Algebra. Addison-Wesley Publishing, Reading, MA and London; Don Mills, Ontario.Google Scholar
Avramidi, G. and Nguyen-Phan, T. T. (2015). Flat cycles in the homology of . Comment. Math. Helv., 90:645–666.Google Scholar
Bass, H. (1964). -theory and stable algebra. Inst. Hautes Études Sci. Publ. Math., 22:5–60.Google Scholar
Bass, H., Milnor, J., and Serre, J.-P. (1967). Solution of the congruence subgroup problem for and . Inst. Hautes Études Sci. Publ. Math., 33:59–137.Google Scholar
Behr, H. (1969). Endliche Erzeugbarkeit arithmetischer Gruppen über Funktionenkörpern. Invent. Math., 7:1–32.Google Scholar
Behr, H. (1975). Explizite Präsentation von Chevalley-gruppen über Z. Math. Z., 141: 235–241.Google Scholar
Biberhofer, S. (2012). On the Cohomology of Arithmetic Subgroups of Unipotent Algebraic Groups. Diplomarbeit, Universität Wien. Fakultät für Mathematik.Google Scholar
Birkes, D. (1971). Orbits of linear algebraic groups. Ann. Math. (2), 93:459–475.Google Scholar
Borek, T. (2005). Successive minima and slopes of Hermitian vector bundles over number fields. J. Number Theory, 113:380–388.Google Scholar
Borel, A. (1961). Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes. Tohoku Math. J. (2), 13:216–240.CrossRefGoogle Scholar
Borel, A. (1963a). Compact Clifford–Klein forms of symmetric spaces. Topology, 2: 111–122.CrossRefGoogle Scholar
Borel, A. (1963b). Some finiteness properties of adele groups over number fields. Inst. Hautes Études Sci. Publ. Math., 16:5–30.Google Scholar
Borel, A. (1969). Introduction aux Groupes Arithmétiques. Publications de l’Institut de Mathématique de l’Université de Strasbourg, XV. Actualités Sci. Indust., No. 1341. Hermann, Paris.Google Scholar
Borel, A. and Harder, G. (1978). Existence of discrete cocompact subgroups of reductive groups over local fields. J. Reine Angew. Math., 298:53–64.Google Scholar
Borel, A. and Harish-Chandra, (1962). Arithmetic subgroups of algebraic groups. Ann. Math. (2), 75:485–535.Google Scholar
Borel, A. and Serre, J.-P. (1964). Théorèmes de finitude en cohomologie galoisienne. Comment. Math. Helv., 39:111–164.Google Scholar
Borel, A. and Serre, J.-P. (1973). Corners and arithmetic groups. Comment. Math. Helv., 48:436–491.Google Scholar
Borel, A. and Serre, J.-P. (1976). Cohomologie d’immeubles et de groupes -arithmétiques. Topology, 15:211–232.CrossRefGoogle Scholar
Borel, A. and Tits, J. (1965). Groupes réductifs. Inst. Hautes Études Sci. Publ. Math., 27:55–150.Google Scholar
Bosch, S., Lütkebohmert, W., and Raynaud, M. (1990). Néron Models. Ergeb. Math. Grenzgeb., 3 volume 21. Springer, Berlin.Google Scholar
Bost, J.-B. and Künnemann, K. (2010). Hermitian vector bundles and extension groups on arithmetic schemes. I. Geometry of numbers. Adv. Math., 223:987–1106.Google Scholar
Bourbaki, N. (1960). Éléments de Mathématique. Première Partie. (Fascicule III.) Livre III; Topologie Générale. Chap. 3: Groupes Topologiques. Chap. 4: Nombres Réels. 3rd ed. Actualités Sci. Indust., No. 1143. Hermann, Paris.Google Scholar
Bourbaki, N. (1985). Éléments de Mathématique. Algèbre Commutative. Chapitres 1 à 4., Reprint. Masson, Paris.Google Scholar
Bruhat, F. and Tits, J. (1967). Groupes algébriques simples sur un corps local. In Proc. Conf. Local Fields (Driebergen, 1966), pages 23–36. Springer, Berlin.Google Scholar
Bruhat, F. and Tits, J. (1972). Groupes réductifs sur un corps local. Inst. Hautes Études Sci. Publ. Math., 41:5–251.Google Scholar
Bruhat, F. and Tits, J. (1984). Groupes réductifs sur un corps local. II. Schémas en groupes. Existence d’une donnée radicielle valuée. Inst. Hautes Études Sci. Publ. Math., 60:197–376.Google Scholar
Cassels, J. W. S. (1967). Global fields. In Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Cassels, J. W. S. and Fröhlich, A. (eds.), pages 42–84. Academic Press, London.Google Scholar
Cassels, J. W. S. (1971). An Introduction to the Geometry of Numbers. 2nd ed. Grundlehren Math. Wiss., Band 99. Springer, Berlin–New York.Google Scholar
Chevalley, C. (1951). Deux théorèmes d’arithmétique. J. Math. Soc. Japan, 3:36–44.Google Scholar
Chevalley, C. (1955). Sur certains groupes simples. Tohoku Math. J. (2), 7:14–66.Google Scholar
Chevalley, C. (1961). Certains schémas de groupes semi-simples. In Séminaire Bourbaki, Vol. 6, Exp. No. 219, pages 219–234. Soc. Math. France, Paris.Google Scholar
Conrad, B. (2012a). Finiteness theorems for algebraic groups over function fields. Compos. Math., 148:555–639.Google Scholar
Conrad, B. (2012b). Weil and Grothendieck approaches to adelic points. Enseign. Math. (2), 58:61–97.Google Scholar
Conrad, B. (2014). Reductive group schemes. In Autour des schémas en groupes. Vol. I. Panor. Synthèses, volume 42/43, pages 93–444. Soc. Math. France, Paris.Google Scholar
Conrad, B., Gabber, O., and Prasad, G. (2010). Pseudo-Reductive Groups, New Math. Monogr., volume 17. Cambridge University Press, Cambridge.Google Scholar
Daw, C. and Orr, M. (2021). Quantitative reduction theory and unlikely intersections. Int. Math. Res. Not. IMRN, rnab173, doi: https://dx.doi.org/10.1093/imrn/rnab173.Google Scholar
Demazure, M. (1965). Schémas en groupes réductifs. Bull. de la Soc. Math. de France, 93:369–413.Google Scholar
Demazure, M. and Gabriel, P. (1970). Groupes Algébriques. Tome I: Géométrie Algébrique, Généralités, Groupes Commutatifs. Masson & Cie, Éditeur, Paris; North-Holland Publishing, Amsterdam.Google Scholar
Deuring, M. (1968). Algebren. 2nd ed. Ergeb. Math. Grenzgeb., Band 41. Springer, Berlin–New York.Google Scholar
Elstrodt, J., Grunewald, F., and Mennicke, J. (1998). Groups Acting on Hyperbolic Space. Springer Monogr. Maths. Springer, Berlin.CrossRefGoogle Scholar
Farrell, F. T., Ontaneda, P., and Raghunathan, M. S. (2000). Non-univalent harmonic maps homotopic to diffeomorphisms. J. Differ. Geom., 54:227–253.Google Scholar
Fricke, R. (1886). Über die Substitutionsgruppen, welche zu den aus dem Legendreschen Integralmodul gezogenen Wurzeln gehören. Math. Ann., 28:99–118.Google Scholar
Fröhlich, A. (1967). Local fields. In Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Cassels, J. W. S. and Fröhlich, A. (eds.), pages 1–41. Academic Press, London.Google Scholar
Gauss, C. F. (1840). Recension der “Untersuchungen über die Eigenschaften der positiven ternären quadratischen Formen von Ludwig August Seeber”. J. Reine Angew. Math., 20:312–320.Google Scholar
Godement, R. (1961). Groupes linéaires algébriques sur un corps parfait. In Séminaire Bourbaki, Vol. 6, Exp. No. 206, pages 11–32. Soc. Math. France, Paris.Google Scholar
Godement, R. (1964). Domaines fondamentaux des groupes arithmétiques. In Séminaire Bourbaki, 1962/63. Fasc. 3, No. 257, pages 201–225. Secrétariat mathématique, Paris.Google Scholar
Grayson, D. (1982). Finite generation of -groups of a curve over a finite field (after Daniel Quillen). In Algebraic -Theory, Part I (Oberwolfach, 1980). Lect. Notes in Maths., volume 966, pages 69–90. Springer, Berlin–New York.Google Scholar
Grayson, D. (1984). Reduction theory using semistability. Comment. Math. Helv., 59: 600–634.Google Scholar
Greub, W., Halperin, S., and Vanstone, R. (1973). Connections, Curvature, and Cohomology. Vol. II: Lie Groups, Principal Bundles, and Characteristic Classes. Pure and Appl. Math., volume 47–II. Academic Press [Harcourt Brace Jovanovich, Publishers], New York–London.Google Scholar
Grothendieck, A. (1957). Sur quelques points d’algèbre homologique. Tohoku Math. J. (2), 9:119–221.Google Scholar
Grunewald, F. and Schwermer, J. (1999). On the concept of level for subgroups of over arithmetic rings. Israel J. Math., 114:205–220.Google Scholar
Guralnick, R. and Lorenz, M. (2006). Orders of finite groups of matrices. In Groups, Rings and Algebras. Contemp. Math., volume 420, pages 141–161. Amer. Math. Soc., Providence, RI.Google Scholar
Harder, G. (1969). Minkowskische Reduktionstheorie über Funktionenkörpern. Invent. Math., 7:33–54.CrossRefGoogle Scholar
Harder, G. (1971). A Gauss–Bonnet formula for discrete arithmetically defined groups. Ann. Sci. École Norm. Sup. (4), 4:409–455.Google Scholar
Harder, G. and Narasimhan, M. S. (1974/75). On the cohomology groups of moduli spaces of vector bundles on curves. Math. Ann., 212:215–248.Google Scholar
Harder, G. and Stuhler, U. (2003). Canonical parabolic subgroups of arakelov group schemes. preprint, pages 1–45.Google Scholar
Hasse, H. (1931). Über -adische Schiefkörper und ihre Bedeutung für die Arithmetik hyperkomplexer Zahlsysteme. Math. Ann., 104:495–534.CrossRefGoogle Scholar
Helgason, S. (1978). Differential Geometry, Lie Groups, and Symmetric Spaces. Pure Appl. Math., volume 80. Academic Press, New York–London.Google Scholar
Hey, K. (1929). Analytische Zahlentheorie in Systemen Hyperkomplexer Zahlen. Lütcke & Wolf, Hamburg.Google Scholar
Hirzebruch, F. (1958). Automorphe Formen und der Satz von Riemann-Roch. In Symposium Internacional de Topologa Algebraica, pages 129–144. Universidad Nacional Autónoma de México and UNESCO, Mexico City.Google Scholar
Hochschild, G. (1961). Cohomology of algebraic linear groups. Illinois J. Math., 5: 492–519.Google Scholar
Hopf, H. and Samelson, H. (1941). Ein Satz über die Wirkungsräume geschlossener Liescher Gruppen. Comment. Math. Helv., 13:240–251.Google Scholar
Humphreys, J. E. (1972). Introduction to Lie Algebras and Representation Theory. Grad. Texts in Maths., volume 9. Springer, New York–Berlin.Google Scholar
Hürlimann, W. (1992). A short proof of the Albert–Brauer–Hasse–Noether theorem. Asterisque, 209:215–220.Google Scholar
Husemoller, D. (1994). Fibre Bundles, 3rd ed. Grad. Texts in Maths., volume 20. Springer, New York.CrossRefGoogle Scholar
Jantzen, J.-C. (2003). Representations of Algebraic Groups, 2nd ed. Math. Surv. Monogr., volume 107. Amer. Math. Soc., Providence, RI.Google Scholar
Jantzen, J.-C. and Schwermer, J. (2014). Algebra. Springer, Berlin–Heidelberg.Google Scholar
Januszewski, F. (2011). Modular symbols for reductive groups and -adic Rankin-Selberg convolutions over number fields. J. Reine Angew. Math., 653:1–45.Google Scholar
Kionke, S. (2012). Lefschetz Numbers of Involutions on Arithmetic Subgroups of Inner Forms of the Special Linear Group. Thesis, Universität Wien. Fakultät für Mathematik.Google Scholar
Kionke, S. (2014). Lefschetz numbers of symplectic involutions on arithmetic groups. Pacific J. Math., 271:369–414.Google Scholar
Knebusch, M. and Scharlau, W. (1971). Quadratische Formen und quadratische Reziprozitätsgesetze über algebraischen Zahlkörpern. Math. Z., 121: 346–368.Google Scholar
Knus, M.-A., Merkurjev, A., Rost, M., and Tignol, J.-P. (1998). The Book of Involutions. Volume 44, Amer. Math. Soc. Colloquium Publications, Providence, RI.Google Scholar
Koch, S. (2017). On the special linear group over orders in quaternion division algebras. J. Number Theory, 181:147–163.Google Scholar
Koszul, J.-L. (1965). Lectures on Groups of Transformations. Lect. Math., No. 32. Tata Institute of Fundamental Research, Bombay.Google Scholar
Lam, T. Y. (1999). Lectures on Modules and Rings. Grad. Texts in Maths., volume 189. Springer, New York.Google Scholar
Lam, T. Y. (2001). A First Course in Noncommutative Rings, 2nd ed. Grad. Texts in Maths., volume 131. Springer, New York.Google Scholar
Landherr, W. (1937). Liesche Ringe vom Typus A über einem algebraischen Zahlkörper (Die lineare Gruppe) und hermitesche Formen über einem Schiefkörper. Abh. Math. Semin. Univ. Hambg., 12:200–241.CrossRefGoogle Scholar
Lee, R. and Schwermer, J. (1986). Geometry and arithmetic cycles attached to . I. Topology, 25:159–174.Google Scholar
Mahler, K. (1938). On Minkowski’s theory of reduction of positive definite quadratic forms. Quarterly J. Math., 9:259–262.Google Scholar
Mendoza, E. (1979). Cohomology of over Imaginary Quadratic Integers. Bonner Mathematische Schriften, 128. Universität Bonn, Math. Institut, Bonn.Google Scholar
Mennicke, J. (1965). Finite factor groups of the unimodular group. Ann. Math. (2), 81:31–37.CrossRefGoogle Scholar
Millson, J. and Raghunathan, M. S. (1981). Geometric construction of cohomology for arithmetic groups. I. Proc. Indian Acad. Sci. Math. Sci., 90:103–123.Google Scholar
Milne, J. S. (2017). Algebraic Groups. Cambridge Stud. Adv. Math., volume 170. Cambridge University Press, Cambridge.Google Scholar
Milnor, J. W. and Stasheff, J. D. (1974). Characteristic Classes. Ann. Math. Stud., No. 76. Princeton University Press, Princeton, NJ.Google Scholar
Minkowski, H. (1887a). Ueber den arithmetischen Begriff der Aequivalenz und über die endlichen Gruppen linearer ganzzahliger Substitutionen. J. Reine Angew. Math., 100:449–458.Google Scholar
Minkowski, H. (1887b). Zur Theorie der positiven quadratischen Formen. J. Reine Angew. Math., 101:196–202.Google Scholar
Minkowski, H. (1896). Geometrie der Zahlen. Bibliotheca Mathematica Teubneriana, Band 40. Johnson Reprint Corp, New York–London.Google Scholar
Minkowski, H. (1905). Diskontinuitätsbereich für arithmetische Äquivalenz. J. Reine Angew. Math., 129:220–274.Google Scholar
Mondal, A. and Sankaran, P. (2019). Geometric cycles in compact locally Hermitian symmetric spaces and automorphic representations. Transform. Groups, 24:913–948.Google Scholar
Mostow, G. D. (1955a). On covariant fiberings of Klein spaces. Amer. J. Math., 77: 247–278.Google Scholar
Mostow, G. D. (1955b). Self-adjoint groups. Ann. Math. (2), 62:44–55.Google Scholar
Mostow, G. D. and Tamagawa, T. (1962). On the compactness of arithmetically defined homogeneous spaces. Ann. Math. (2), 76:446–463.Google Scholar
Naumann, N. (2008). Arithmetically defined dense subgroups of Morava stabilizer groups. Compos. Math., 144:247–270.Google Scholar
Neukirch, J. (1999). Algebraic Number Theory. Grundlehren Math. Wiss., volume 322. Springer, Berlin.Google Scholar
Nomizu, K. (1954). On the cohomology of compact homogeneous spaces of nilpotent Lie groups. Ann. Math. (2), 59:531–538.Google Scholar
Oesterlé, J. (1984). Nombres de Tamagawa et groupes unipotents en caractéristique . Invent. Math., 78:13–88.Google Scholar
O’Meara, O. T. (1963). Introduction to Quadratic Forms. Grundlehren Math. Wiss., Band 117. Springer, Berlin–Göttingen–Heidelberg.Google Scholar
Ono, T. (1961). Arithmetic of algebraic tori. Ann. Math. (2), 74:101–139.Google Scholar
Pick, G. (1886). Über gewisse ganzzahlige lineare substitutionen, welche sich nicht durch algebraische congruenzen erklären lassen. Math. Ann., 28:119–124.Google Scholar
Quillen, D. (1971). Elementary proofs of some results of cobordism theory using Steenrod operations. Adv. Math., 7:29–56.Google Scholar
Raghunathan, M. S. (1972). Discrete Subgroups of Lie Groups. Ergeb. Math. Grenzgeb., volume 68. Springer, New York–Heidelberg.Google Scholar
Raghunathan, M. S. (1982). Arithmetic lattices in semisimple groups. Proc. Indian Acad. Sci. Math. Sci., 91:133–138.Google Scholar
Reiner, I. (2003). Maximal Orders. London Math. Soc. Monogr. New Series, volume 28. Corrected reprint. The Clarendon Press, Oxford.Google Scholar
Rohlfs, J. (1981). The Lefschetz number of an involution on the space of classes of positive definite quadratic forms. Comment. Math. Helv., 56:272–296.Google Scholar
Rohlfs, J. (1985). On the cuspidal cohomology of the Bianchi modular groups. Math. Z., 188:253–269.Google Scholar
Rohlfs, J. (1990). Lefschetz numbers for arithmetic groups. In Cohomology of Arithmetic Groups and Automorphic Forms (Luminy–Marseille, 1989). Lect. Notes in Math., volume 1447, pages 303–313. Springer, Berlin.Google Scholar
Rohlfs, J. and Schwermer, J. (1993). Intersection numbers of special cycles. J. Amer. Math. Soc., 6:755–778.Google Scholar
Rohlfs, J. and Schwermer, J. (1998). An arithmetic formula for a topological invariant of Siegel modular varieties. Topology, 37:149–159.Google Scholar
Rohlfs, J. and Speh, B. (1989). Automorphic representations and Lefschetz numbers. Ann. Sci. École Norm. Sup. (4), 22:473–499.Google Scholar
Scharlau, W. (1985). Quadratic and Hermitian Forms. Grundlehren Math. Wiss., volume 270. Springer, Berlin.Google Scholar
Schimpf, S. (2012). On the Geometric Construction of Cohomology Classes for Cocompact Discrete Subgroups of the Real and Complex Special Linear Group. Thesis, Universität Wien. Fakultät für Mathematik.Google Scholar
Schimpf, S. (2016). On the geometric construction of cohomology classes for cocompact discrete subgroups of and . Pacific J. Math., 282:445–477.Google Scholar
Schwermer, J. (1991). Räumliche Anschauung und Minima positiv definiter quadratischer Formen. Zur Habilitation von Hermann Minkowski 1887 in Bonn. Jahresber. Deutsch. Math.-Verein., 93:49–105.Google Scholar
Schwermer, J. (2007). Reduction theory of quadratic forms: towards räumliche Anschauung in Minkowski’s early work. In The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae, pages 483–504. Springer, Berlin.Google Scholar
Schwermer, J. (2010). Geometric cycles, arithmetic groups and their cohomology. Bull. Amer. Math. Soc. (N.S.), 47:187–279.Google Scholar
Schwermer, J. (2011). Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups. Groups Geom. Dyn., 5:529–552.CrossRefGoogle Scholar
Schwermer, J. and Vogtmann, K. (1983). The integral homology of and of Euclidean imaginary quadratic integers. Comment. Math. Helv., 58:573–598.Google Scholar
Schwermer, J. and Vukadin, O. (2011). The stable rank of arithmetic orders in division algebras—an elementary approach. Enseign. Math. (2), 57:155–163.Google Scholar
Schwermer, J. and Waldner, C. (2016). Geometric cycles, classical groups and related cohomology classes for arithmetic groups. In Advances in the Theory of Automorphic Forms and Their -Functions. Contemp. Math., volume 664, pages 367–376. Amer. Math. Soc., Providence, RI.Google Scholar
Serre, J.-P. (1968). Corps Locaux. Hermann, Paris. Deuxième édition, Publications de l’Université de Nancago, No. VIII.Google Scholar
Serre, J.-P. (1970). Le problème des groupes de congruence pour . Ann. Math. (2), 92:489–527.Google Scholar
Serre, J.-P. (1971). Cohomologie des groupes discrets. In Prospects in Mathematics. Ann. of Math. Studies, volume 70, pages 77–169. Princeton University Press, Princeton, NJ.Google Scholar
Serre, J.-P. (1977). Arbres, Amalgames, . Astérisque, volume 46. Société Mathématique de France, Paris.Google Scholar
Serre, J.-P. (1994). Cohomologie Galoisienne, 5th ed. Lect. Notes in Maths., volume 5. Springer, Berlin.Google Scholar
Serre, J.-P. (2007). Bounds for the orders of the finite subgroups of. In Group Representation Theory, pages 405–450. EPFL Press, Lausanne.Google Scholar
SGA. (1970). Schémas en groupes. I–III. In Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lect. Notes in Maths., volume 151–153. Springer, Berlin–New York.Google Scholar
Siegel, C. L. (1939). Einheiten quadratischer Formen. Abh. Math. Sem. Univ. Hamburg, 13:209–239.Google Scholar
Siegel, C. L. (1959). Zur Reduktionstheorie Quadratischer Formen. Publ. Math. Soc. Japan, volume 5. The Mathematical Society of Japan, Tokyo.Google Scholar
Siegel, C. L. (1965). Lectures on Advanced Analytic Number Theory. Notes by Raghavan, S.. Lect. in Math., No. 23. Tata Institute of Fundamental Research, Bombay.Google Scholar
Springer, T. A. (1994). Reduction theory over global fields. Proc. Indian Acad. Sci. Math. Sci., 104:207–216.Google Scholar
Springer, T. A. (1998). Linear Algebraic Groups, 2nd ed. Prog. Math., volume 9. Birkhäuser Boston, Boston, MA.Google Scholar
Steinberg, R. (1968). Endomorphisms of Linear Algebraic Groups. Memoirs of the Amer. Math. Soc., No. 80. Amer. Math. Soc., Providence, RI.CrossRefGoogle Scholar
Steinberg, R. (2016). Lectures on Chevalley groups, volume 66 of University Lecture Series. Revised and corrected edition of the 1968 original. Amer. Math. Soc., Providence, RI.Google Scholar
Stuhler, U. (1976). Eine Bemerkung zur Reduktionstheorie quadratischer Formen. Arch. Math., 27:604–610.CrossRefGoogle Scholar
Stuhler, U. (1977). Zur Reduktionstheorie der positiven quadratischen Formen. II. Arch. Math., 28:611–619.Google Scholar
Tate, J. (1966). The cohomology groups of tori in finite Galois extensions of number fields. Nagoya Math. J., 27:709–719.CrossRefGoogle Scholar
Tits, J. (1966). Sur les constantes de structure et le théorème d’existence des algèbres de Lie semi-simples. Inst. Hautes Études Sci. Publ. Math., 31:21–58.Google Scholar
Tits, J. (1979). Reductive groups over local fields. In Automorphic Forms, Representations and -Functions, Part 1, Proc. Sympos. Pure Math., XXXIII, pages 29–69. Amer. Math. Soc., Providence, RI.Google Scholar
Tshishiku, B. (2021). Geometric cycles and characteristic classes of manifold bundles. Comment. Math. Helv., 96:1–45. With an appendix by M. Krannich.Google Scholar
van der Waerden, B. L. (1940). Moderne Algebra. Springer, Berlin.CrossRefGoogle Scholar
van der Waerden, B. L. (1956). Die Reduktionstheorie der positiven quadratischen Formen. Acta Math., 96:265–309.Google Scholar
van Est, W. T. (1958). A generalization of the Cartan–Leray spectral sequence. I, II. Nederl. Akad. Wetensch. Proc. Ser. A (Indag. Math.), 20:399–413.Google Scholar
Vogtmann, K. (1985). Rational homology of Bianchi groups. Math. Ann., 272:399–419.Google Scholar
Voskresenski, V. E. (1998). Algebraic Groups and Their Birational Invariants. Transl. Math. Monogr., volume 179. Amer. Math. Soc., Providence, RI.Google Scholar
Waldner, C. (2010). Geometric cycles and the cohomology of arithmetic subgroups of the exceptional group . J. Topol., 3:81–109.Google Scholar
Weil, A. (1964). Sur certains groupes d’opérateurs unitaires. Acta Math., 111:143–211.Google Scholar
Weil, A. (1967). Basic Number Theory. Grundlehren Math. Wiss., Band. 144. Springer, New York.Google Scholar
Weil, A. (1982). Adeles and Algebraic Groups. Prog. Math., volume 23. Birkhäuser, Boston, MA.Google Scholar
Weyl, H. (1940). Theory of reduction for arithmetical equivalence. Trans. Amer. Math. Soc., 48:126–164.Google Scholar
Zschumme, P. (2021). Geometric construction of homology classes in Riemannian manifolds covered by products of hyperbolic planes. Geom. Dedicata, 213:191–210.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Joachim Schwermer, Universität Wien, Austria
  • Book: Reduction Theory and Arithmetic Groups
  • Online publication: 01 December 2022
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Joachim Schwermer, Universität Wien, Austria
  • Book: Reduction Theory and Arithmetic Groups
  • Online publication: 01 December 2022
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Joachim Schwermer, Universität Wien, Austria
  • Book: Reduction Theory and Arithmetic Groups
  • Online publication: 01 December 2022
Available formats
×