Duke Mathematical Journal
previous :: next

Lefschetz classes on abelian varieties

J. S. Milne
Source: Duke Math. J. Volume 96, Number 3 (1999), 639-675.
First Page: Show Hide
Primary Subjects: 14C25
Secondary Subjects: 11G10, 14C30, 14K05
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077229328
Mathematical Reviews number (MathSciNet): MR1671217
Zentralblatt MATH identifier: 0976.14009
Digital Object Identifier: doi:10.1215/S0012-7094-99-09620-5

References

[B] Armand Borel, Linear algebraic groups, Graduate Texts in Mathematics, vol. 126, Springer-Verlag, New York, 1991, 2d ed.
Mathematical Reviews (MathSciNet): MR92d:20001
Zentralblatt MATH: 0726.20030
[D] P. Deligne, “Hodge cycles on abelian varieties (notes by J. S. Milne)”, Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math., vol. 900, Springer-Verlag, Berlin, 1982, pp. 9–100.
Zentralblatt MATH: 0537.14006
[F] William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984.
Mathematical Reviews (MathSciNet): MR85k:14004
Zentralblatt MATH: 0541.14005
[FH] William Fulton and Joe Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991, A First Course.
Mathematical Reviews (MathSciNet): MR93a:20069
Zentralblatt MATH: 0744.22001
[G] A. Grothendieck, Standard conjectures on algebraic cycles, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968), Oxford Univ. Press, London, 1969, pp. 193–199.
Mathematical Reviews (MathSciNet): MR42:3088
Zentralblatt MATH: 0201.23301
[H] Fumio Hazama, Algebraic cycles on certain abelian varieties and powers of special surfaces, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1985), no. 3, 487–520.
Mathematical Reviews (MathSciNet): MR86k:14004
Zentralblatt MATH: 0591.14006
[I] Takashi Ichikawa, Algebraic groups associated with abelian varieties, Math. Ann. 289 (1991), no. 1, 133–142.
Mathematical Reviews (MathSciNet): MR92f:14043
Zentralblatt MATH: 0697.14031
Digital Object Identifier: doi:10.1007/BF01446564
[Kl] S. L. Kleiman, Algebraic cycles and the Weil conjectures, Dix esposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968, pp. 359–386.
Mathematical Reviews (MathSciNet): MR45:1920
Zentralblatt MATH: 0198.25902
[Kn] Max-Albert Knus, Quadratic and Hermitian forms over rings, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 294, Springer-Verlag, Berlin, 1991.
Mathematical Reviews (MathSciNet): MR92i:11039
Zentralblatt MATH: 0756.11008
[Ku] Klaus Künnemann, On the Chow motive of an abelian scheme, Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 189–205.
Mathematical Reviews (MathSciNet): MR95d:14009
Zentralblatt MATH: 0823.14032
[LZ] Hendrik W. Lenstra, Jr. and Yuri G. Zarhin, The Tate conjecture for almost ordinary abelian varieties over finite fields, Advances in number theory (Kingston, ON, 1991), Oxford Sci. Publ., Oxford Univ. Press, New York, 1993, pp. 179–194.
Mathematical Reviews (MathSciNet): MR97c:11067
Zentralblatt MATH: 0817.14022
[Li] David I. Lieberman, Numerical and homological equivalence of algebraic cycles on Hodge manifolds, Amer. J. Math. 90 (1968), 366–374.
Mathematical Reviews (MathSciNet): MR37:5898
Zentralblatt MATH: 0159.50501
Digital Object Identifier: doi:10.2307/2373533
[M1] J. S. Milne, Abelian varieties, Arithmetic geometry (Storrs, Conn., 1984), Springer, New York, 1986, pp. 103–150.
Mathematical Reviews (MathSciNet): MR861974
Zentralblatt MATH: 0604.14028
[M2] J. S. Milne, On the conjecture of Langlands and Rapoport, (preprint preliminary version), Sept. 25, 1995.
[M3] J. S. Milne, Lefschetz motives and the Tate conjecture, to appear in Compositio Math.
Mathematical Reviews (MathSciNet): MR1692999
Zentralblatt MATH: 0985.14010
Digital Object Identifier: doi:10.1023/A:1000776613765
[Mum] David Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, No. 5, Published for the Tata Institute of Fundamental Research, Bombay, 1970.
Mathematical Reviews (MathSciNet): MR44:219
Zentralblatt MATH: 0223.14022
[Mur] V. Kumar Murty, Exceptional Hodge classes on certain abelian varieties, Math. Ann. 268 (1984), no. 2, 197–206.
Mathematical Reviews (MathSciNet): MR85m:14063
Zentralblatt MATH: 0521.14004
Digital Object Identifier: doi:10.1007/BF01456085
[R] Kenneth A. Ribet, Hodge classes on certain types of abelian varieties, Amer. J. Math. 105 (1983), no. 2, 523–538.
Mathematical Reviews (MathSciNet): MR85a:14030
Zentralblatt MATH: 0586.14003
Digital Object Identifier: doi:10.2307/2374267
[S] Chad Schoen, Hodge classes on self-products of a variety with an automorphism, Compositio Math. 65 (1988), no. 1, 3–32.
Mathematical Reviews (MathSciNet): MR89c:14013
Zentralblatt MATH: 0663.14006
[Sch] A. J. Scholl, Classical motives, Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 163–187.
Mathematical Reviews (MathSciNet): MR95b:11060
Zentralblatt MATH: 0814.14001
[Se] Jean-Pierre Serre, Groupes algébriques et corps de classes, Publications de l'institut de mathématique de l'université de Nancago, VII. Hermann, Paris, 1959.
Mathematical Reviews (MathSciNet): MR21:1973
Zentralblatt MATH: 0097.35604
[T] S. G. Tankeev, Cycles on simple abelian varieties of prime dimension, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 1, 155–170, 192, (in Russian).
Mathematical Reviews (MathSciNet): MR83e:14017
Zentralblatt MATH: 0587.14005
[Ta1] John Tate, Endomorphisms of abelian varieties over finite fields, Invent. Math. 2 (1966), 134–144.
Mathematical Reviews (MathSciNet): MR34:5829
Zentralblatt MATH: 0147.20303
Digital Object Identifier: doi:10.1007/BF01404549
[Ta2] John Tate, Conjectures on algebraic cycles in $l$-adic cohomology, Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 71–83.
Mathematical Reviews (MathSciNet): MR95a:14010
Zentralblatt MATH: 0814.14009
[Wei] W. Wei, Weil numbers and generating large field extensions, thesis, Univ. of Michigan, Ann Arbor, Mich., 1993.
[W1] André Weil, Algebras with involutions and the classical groups, J. Indian Math. Soc. (N.S.) 24 (1960), 589–623 (1961).
Mathematical Reviews (MathSciNet): MR25:147
Zentralblatt MATH: 0109.02101
[W2] A. Weil, “Abelian varieties and Hodge ring”, Collected Papers, Vol. III, Springer-Verlag, Berlin, 1977, pp. 421–429.
[We] Hermann Weyl, The Classical Groups. Their Invariants and Representations, Princeton University Press, Princeton, N.J., 1939, 2d ed.
Mathematical Reviews (MathSciNet): MR1,42c
Zentralblatt MATH: 0020.20601
[Wh] Samuel P. White, Sporadic cycles on CM abelian varieties, Compositio Math. 88 (1993), no. 2, 123–142.
Mathematical Reviews (MathSciNet): MR94i:14048
Zentralblatt MATH: 0798.14025
[Z1] Yuri G. Zarhin, Abelian varieties of $K3$ type and $l$-adic representations, Algebraic geometry and analytic geometry (Tokyo, 1990), ICM-90 Satell. Conf. Proc., Springer, Tokyo, 1991, pp. 231–255.
Mathematical Reviews (MathSciNet): MR94i:14047
Zentralblatt MATH: 0788.14039
[Z2] Yu. G. Zarhin, The Tate conjecture for nonsimple abelian varieties over finite fields, Algebra and number theory (Essen, 1992), de Gruyter, Berlin, 1994, pp. 267–296.
Mathematical Reviews (MathSciNet): MR95c:11078
Zentralblatt MATH: 0831.14019
previous :: next

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?