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
×
  1. Home
  2. Books
  3. Lectures on Algebraic Cycles
  • Cited by 23
Publisher:
Cambridge University Press
Online publication date:
July 2014
Print publication year:
2010
Online ISBN:
9780511760693
DOI:
https://doi.org/10.1017/CBO9780511760693
Subjects:
Mathematics (general), Mathematics, Number Theory, Geometry and Topology
Series:
New Mathematical Monographs (16)
Information

Book description

Spencer Bloch's 1979 Duke lectures, a milestone in modern mathematics, have been out of print almost since their first publication in 1980, yet they have remained influential and are still the best place to learn the guiding philosophy of algebraic cycles and motives. This edition, now professionally typeset, has a new preface by the author giving his perspective on developments in the field over the past 30 years. The theory of algebraic cycles encompasses such central problems in mathematics as the Hodge conjecture and the Bloch–Kato conjecture on special values of zeta functions. The book begins with Mumford's example showing that the Chow group of zero-cycles on an algebraic variety can be infinite-dimensional, and explains how Hodge theory and algebraic K-theory give new insights into this and other phenomena.

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
Bibliography
Artin, M. and B., Mazur, Formal groups arising from algebraic varieties, Ann. Sci. École Norm. Sup. (4), 10 (1977 CrossRef | Google Scholar), 87-132.
Atiyah, M. and F., Hirzebruch, Analytic cycles on complex manifolds, Topology, 1 (1962 Google Scholar) 25–45.
Bass, H.Algebraic K-Theory, Benjamin, New York (1968 Google Scholar).
Bass, H. and J., Tate, The Milnor ring of a global field, in Algebraic K-Theory II, Lecture Notes in Math., no. 342, Springer, Berlin (1973 Google Scholar).
Beauville, A.Variétés de Prym et jacobiennes intermédiaries, Ann. Sci. Ecole Norm. Sup. (4), 10 (1977 Google Scholar), 304-391.
Beauville, A.Surfaces algébriques complexes, Astérisque, 59 (1978 Google Scholar),
Bloch, S.K2 and algebraic cycles, Ann. of Math. (2), 99 (1974 CrossRef | Google Scholar), 349-379.
Bloch, S.Torsion algebraic cycles, K2, and Brauer groups of function fields, Bull. Amer. Math. Soc., 80 (1974 CrossRef | Google Scholar), 941-945.
Bloch, S.K2 of Artinian Q-algebras with application to algebraic cycles, Comm. Algebra, 3 (1975 Google Scholar), 405-428.
Bloch, S.An example in the theory of algebraic cycles, pp. 1-29 in Algebraic K-Theory, Lecture Notes in Math., no. 551, Springer, Berlin (1976 Google Scholar).
Bloch, S.Some elementary theorems about algebraic cycles on abelian varieties, Invent. Math., 37 (1976 Google Scholar), 215-228.
Bloch, S.Algebraic K-theory and crystalline cohomology, Inst. Hautes Etudes Sci. Publ. Math., no. 47 (1977 Google Scholar), 187-268 (1978).
Bloch, S.Applications of the dilogarithm function in algebraic K-theory and algebraic geometry, pp. 103-114 in Proceedings ofthe International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Book Store, Tokyo (1978 Google Scholar).
Bloch, S.Higher Regulators, Algebraic K-Theory, and Zeta Functions of Elliptic Curves, Lectures given at the University of California, Irvine (1978). [CRM Monograph Series, no. 11, American Mathematical Society, Providence, R.I., 2000 Google Scholar.]
Bloch, S.Some formulas pertaining to the K-theory of commutative group schemes, J. Algebra, 53 (1978 Google Scholar), 304-326.
Bloch, S.Torsion algebraic cycles and a theorem of Roitman, Compositio Math., 39 (1979 Google Scholar), 107-127.
Bloch, S., A., Kas, and D., Lieberman, Zero cycles on surfaces with Pg = 0, Compositio Math., 33 (1976 Google Scholar), 135-145,
Bloch, S. and J. P., Murre, On the Chow groups of certain types of Fano three-folds, Compositio Math., 39 (1979 Google Scholar), 47-105.
Bloch, S. and A., Ogus, Gersten's conjecture and the homology of schemes, Ann. Sci. École Norm. Sup. (4), 7 (1974), 181-201 (1975 Google Scholar).
Borel, A.Cohomologie de SLn et valeurs de fonctions zeta aux points entiers, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 4 (1977 Google Scholar), 613-636; errata, 7 (1980), 373.
Châtelet, F.Points rationnels sur certaines courbes et surfaces cubiques, Enseignement Math. (2), 5 (1959), 153-170 (1960 Google Scholar).
Chevalley, C. et al., Anneaux de Chow et applications, Séminaire C. Chevalley, 2e année, Sécr. Math. Paris (1958 Google Scholar).
Chow, W. L.On equivalence classes of cycles in an algebraic variety, Ann. of Math. (2), 64, 450-479 (1956 Google Scholar).
Clemens, C. H. and P. A., Griffiths, The intermediate Jacobian of the cubic threefold, Ann. of Math. (2), 95 (1972 CrossRef | Google Scholar), 281-356.
Colliot-Thélène, J.-L. and J.-J., Sansuc, Series of notes on rational varieties and groups of multiplicative type, C. R. Acad. Sci. Paris Ser. A-B, 282 (1976 Google Scholar), A1113-A1116; 284 (1977), A967-A970; 284 (1977), A1215-A1218; 287 (1978), A449-A452.
Colliot-Thélène, J.-L. and J.-J., Sansuc, La R-équivalence sur les tores, Ann. Sci. Ecole Norm. Sup. (4), 10 (1977 CrossRef | Google Scholar), 175-229.
Colliot-Thélène, J.-L. and D., Coray, L'équivalence rationnelle sur les points fermes des surfaces rationnelles fibrees en coniques, Compositio Math., bf 39 (1979 Google Scholar), 301-332.
Deligne, P.Théorie de Hodge. I, pp. 425-430 in Actes du Congres International des Mathematiciens (Nice, 1970), vol. 1, Gauthier-Villars, Paris (1971 Google Scholar).
Deligne, P.Théorie de Hodge III, Inst. Hautes Etudes Sci. Publ. Math., no. 44 (1974 Google Scholar), 5-77.
Deligne, P.Poids dans la cohomologie des varietes algebriques, pp. 79-85 in Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974), vol. 1 (1975 Google Scholar).
Deligne, P.Cohomologie étale (SGA 4½), Lecture Notes in Math., no. 569, Springer, Berlin (1977 Google Scholar).
Elman, R. and T. Y., Lam, On the quaternion symbol homomorphism gF: k2(F) → B(F), in Algebraic K-Theory II, Lecture Notes in Math., no. 342, Springer, Berlin (1973 Google Scholar).
Fatemi, T. L'equivalence rationelle des zéro cycles sur les surfaces algébriques complexes a cup product surjectif, These du 3e cycle, Université de Paris VII (1979 Google Scholar).
Fulton, W.Rational equivalence on singular varieties, Inst. Hautes Études Sci. Publ. Math., no. 45 (1975 Google Scholar), 147-167.
Fulton, W. and R., MacPherson, Intersecting cycles on an algebraic variety, Aarhus Universitet Preprint Series, no. 14 (1976). [Pp. 179-197 in Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), Sijthoff and Noordhoff, Alphen aan den Rijn (1977 Google Scholar).]
Gersten, S. M.Some exact sequences in the higher K-theory of rings, pp. 211-243 in Algebraic K-Theory I, Lecture Notes in Math., no. 341, Springer, Berlin (1973 Google Scholar).
Gillet, H.Applications of algebraic K-theory to intersection theory, Thesis, Harvard (1978 Google Scholar).
Griffiths, P.On the periods of certain rational integrals. I, II, Ann. of Math. (2), 90 (1969 Google Scholar), 460-495; 90 (1969), 496-541.
Griffiths, P. and J., Harris, Principles of Algebraic Geometry, Wiley, New York Google Scholar (1978). [Reprinted 1994.]
Grothendieck, A.Le groupe de Brauer I, II, III, pp. 46-188 in Dix exposés sur la cohomologie des schémas, North Holland, Amsterdam (1968 Google Scholar).
Grothendieck, A. et al., Théorie des intersections et théorème de Riemann–Roch (SGA 6), Lecture Notes in Math., no. 225, Springer, Berlin (1971 Google Scholar).
Hartshorne, R.On the de Rham cohomology of algebraic varieties, Inst. Hautes Etudes Sci. Publ. Math., no. 45 (1975 Google Scholar), 5-99.
Inose, H. and M., Mizukami, Rational equivalence of 0-cycles on some surfaces of general type with pg = 0, Math. Ann., 244 (1979 Google Scholar), no. 3, 205-217.
Kleiman, S.Algebraic cycles and the Weil conjectures, pp. 359-386 in Dix exposés sur la cohomologie des schémas, North Holland, Amsterdam (1968 Google Scholar).
Lam, T. Y.The Algebraic Theory of Quadratic Forms, W. A. Benjamin, Reading, Mass. (1973 Google Scholar). [Revised second printing, 1980. See also Introduction to Quadratic Forms over Fields, American Mathematical Society, Providence, R.I., 2005.]
Lang, S.Abelian Varieties, Interscience Publishers (1959 Google Scholar). [Reprinted Springer, 1983.]
Lang, S.Elliptic Functions, Addison-Wesley, Reading, Mass. (1973 Google Scholar). [Second edition: Springer, New York, 1987.]
Lieberman, D. I.Higher Picard varieties, Amer. J. Math., 90 (1968 CrossRef | Google Scholar), 1165-1199.
Manin, Yu.Le groupe de Brauer–Grothendieck en géométrie diophantienne, pp. 401-411 in Actesdu Congrès International Mathématiciens (Nice, 1970), vol. 1, Gauthier-Villars, Paris (1971 Google Scholar).
Manin, Yu.Cubic Forms, North Holland, Amsterdam (1974 Google Scholar). [Second edition, 1986.]
Mattuck, A.Ruled surfaces and the Albanese mapping, Bull. Amer. Math. Soc., 75 (1969 CrossRef | Google Scholar), 776-779.
Mattuck, A.On the symmetric product of a rational surface, Proc. Amer. Math. Soc., 21 (1969 Google Scholar), 683-688.
Milnor, J.Algebraic K-theory and quadratic forms, Invent. Math., 9 (1970 CrossRef | Google Scholar), 318-344.
Milnor, J.Introduction to Algebraic K-Theory, Annals of Mathematics Studies, vol. 72, Princeton University Press, Princeton, N.J. (1971 Google Scholar).
Mumford, D.Rational equivalence of zero-cycles on surfaces, J. Math. Kyoto Univ., 9 (1968 Google Scholar), 195-204,
Murre, J. P.Algebraic equivalence modulo rational equivalence on a cubic threefold, Compositio Math., 25 (1972 Google Scholar), 161-206.
Nakayama, T.Cohomology of class field theory and tensor product modules I, Ann. of Math. (2), 65 (1957 CrossRef | Google Scholar), 255-267.
Quillen, D.Higher algebraic K-theory. I, in Algebraic K-Theory I, Lecture Notes in Math., no. 341, Springer, Berlin (1973 Google Scholar).
Quillen, D. and D., Grayson, Higher algebraic K-theory. II, pp. 217-240 in Algebraic K-Theory, Lecture Notes in Math., no. 551, Springer, Berlin (1976 Google Scholar).
Roitman, A. A.Γ-equivalence of zero-dimensional cycles (in Russian), Mat. Sb. (N.S.), 86 (128) (1971 Google Scholar), 557-570. [Translation: Math USSR-Sb., 15 (1971), 555-567.]
Roitman, A. A.Rational equivalence of zero-dimensional cycles (in Russian), Mat. Sb. (N.S.), 89 (131) (1972 Google Scholar), 569-585, 671. [Translation: Math. USSR-Sb., 18 (1974), 571-588.]
Rosenlicht, M.Generalized Jacobian varieties, Ann. of Math., 59 (1954 CrossRef | Google Scholar), 505-530.
Samuel, P.Rational equivalence of arbitrary cycles, Amer. J. Math., 78 (1956 CrossRef | Google Scholar), 383-400.
Serre, J.-P.Sur la topologie des variétés algebriques en caractéristique p, pp. 24-53 in Symposium Internacional de Topologia Algebraica, Universidad Nacional Autónoma de Mexico and UNESCO, Mexico City (1958 Google Scholar).
Serre, J.-P.. Groupes algébriques et corps de classes, Hermann, Paris (1959 Google Scholar). [Second edition, 1975; reprinted, 1984.]
Serre, J.-P.Algèbre locale. Multiplictés, Lecture Notes in Math., no. 11, Springer, Berlin (1965 Google Scholar).
Serre, J.-P.Corps Locaux, second edition, Hermann, Paris (1968 Google Scholar). [Translation: Local Fields, Springer, New York, 1979.]
Sherman, C.K-cohomology of regular schemes, Comm. Algebra, 7 (1979 Google Scholar), 999-1027.
Stienstra, J.Deformations of the second Chow group, Thesis, Utrecht (1978 Google Scholar).
Stienstra, J.The formal completion of the second Chow group: a K-theoretic approach, pp. 149-168 in Journée de Géométrie Algebrique de Rennes (Rennes, 1978), Vol. II, Asterisque, 64 (1979 Google Scholar).
Swan, R.Algebraic K-Theory, Lecture Notes in Math., no. 76, Springer, Berlin (1968 Google Scholar).
Tate, J.Relations between K2 and Galois cohomology, Invent. Math., 36 (1976 CrossRef | Google Scholar), 257-274.
Tennison, B. R.On the quartic threefold, Proc. London Math. Soc. (3), 29 (1974 Google Scholar), 714-734.
Tyurin, A. N.Five lectures on three-dimensional varieties (in Russian), Uspehi Mat. Nauk, 27 (1972 Google Scholar), no. 5, (167) 3-50. [Translation: Russian Math. Surveys, 27 (1972), no. 5, 1-53.]
Verdier, J.-L.Dualité dans la cohomologie des espaces localement compacts, Séminaire Bourbaki, Vol. 9, exposé no. 300 (1965 Google Scholar), 337-349. [Reprinted Société Mathématique de France, Paris, 1995.]
Verdier, J.-L.A duality theorem in the etale cohomology of schemes, pp. 184-198 in Proceedings of a conference on local fields (Driebergen, 1966), Springer, Berlin (1967 Google Scholar).
Wallace, A.Homology Theory on Algebraic Varieties, Pergamon Press, New York (1958 Google Scholar).
Weil, A.Foundations of Algebraic Geometry, A.M.S. Colloquium Publications, vol. 29, American Mathematical Society, Providence, R.I. (1946 Google Scholar).
Weil, A.Courbes Algébriques et Variétés Abéliennes, Hermann, Paris (1971 Google Scholar).

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.