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2014 | 12 | 5 | 659-674
Tytuł artykułu

Abelian varieties over fields of finite characteristic

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EN
The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.
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Czasopismo
Rocznik
Tom
12
Numer
5
Strony
659-674
Opis fizyczny
Daty
wydano
2014-05-01
online
2014-02-15
Bibliografia
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  • [11] Serre J.-P., Sur les groupes des congruence des variétés abéliennes, Izv. Akad. Nauk SSSR Ser. Mat., 1964, 28, 3–20
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  • [14] Serre J.-P., Abelian ℓ-Adic Representations and Elliptic Curves, 2nd ed., Advanced Book Classics, Addison-Wesley, Redwood City, 1989
  • [15] Skorobogatov A.N., Zarhin Yu.G., A finiteness theorem for the Brauer group of abelian varieties and K3 surfaces, J. Algebraic Geometry, 2008, 17(3), 481–502 http://dx.doi.org/10.1090/S1056-3911-07-00471-7
  • [16] Tate J., Endomorphisms of abelian varieties over finite fields, Invent. Math., 1966, 2, 134–144 http://dx.doi.org/10.1007/BF01404549
  • [17] Zarhin Ju.G., Endomorphisms of Abelian varieties over fields of finite characteristic, Math. USSR-Izv., 1975, 9, 255–260 http://dx.doi.org/10.1070/IM1975v009n02ABEH001476
  • [18] Zarkhin Yu.G., Abelian varieties in characteristic p, Math. Notes, 1976, 19(3), 240–244 http://dx.doi.org/10.1007/BF01437858
  • [19] Zarkhin Yu.G., Endomorphisms of Abelian varieties and points of finite order in characteristic p, Math. Notes, 1977, 21(6), 415–419 http://dx.doi.org/10.1007/BF01410167
  • [20] Zarkhin Yu.G., Torsion of Abelian varieties in fininite characteristic, Math. Notes, 1977, 22(1), 493–498 http://dx.doi.org/10.1007/BF01147687
  • [21] Zarkhin Yu.G., Homomorphisms of Abelian varieties and points of finite order over fields of finite characteristic, In: Problems in Group Theory and Homological Algebra, Yaroslav. Gos. Univ., Yaroslavl, 1981, 146–147 (in Russian)
  • [22] Zarhin Yu.G., A finiteness theorem for unpolarized Abelian varieties over number fields with prescribed places of bad reduction, Invent. Math., 1985, 79(2), 309–321 http://dx.doi.org/10.1007/BF01388976
  • [23] Zarhin Yu.G., Endomorphisms and torsion of abelian varieties, Duke Math. J., 1987, 54(1), 131–145 http://dx.doi.org/10.1215/S0012-7094-87-05410-X
  • [24] Zarhin Yu.G., Hyperelliptic Jacobians without complex multiplication in positive characteristic, Math. Res. Lett., 2001, 8(4), 429–435 http://dx.doi.org/10.4310/MRL.2001.v8.n4.a3
  • [25] Zarkhin Yu.G., Endomorphism rings of certain Jacobians in finite characteristic, Sb. Math., 2002, 193(8), 1139–1149 http://dx.doi.org/10.1070/SM2002v193n08ABEH000673
  • [26] Zarhin Yu.G., Non-supersingular hyperelliptic Jacobians, Bull. Soc. Math. France, 2004, 132(4), 617–634
  • [27] Zarhin Yu.G., Homomorphisms of abelian varieties over finite fields, In: Higher-Dimensional Geometry over Finite Fields, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 16, IOS Press, Amsterdam, 2008, 315–343
  • [28] Zarhin Yu.G., Homomorphisms of abelian varieties over geometric fields of finite characteristic, J. Inst. Math. Jussieu, 2013, 12(2), 225–236 http://dx.doi.org/10.1017/S1474748012000655
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0370-1
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