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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 2, Pages 272–277 (Mi izv1830)  

This article is cited in 5 scientific papers (total in 5 papers)

Endomorphisms of abelian varieties over fields of finite characteristic

Yu. G. Zarhin


Abstract: The semisimplicity of $l$-adic representations corresponding to one-dimensional étale cohomology, and a proof of the Tate's conjecture about homomorphisms of abelian varieties, are derived from the Tate's finiteness conjecture on isogenies of polarized abelian varieties.
Bibliography: 4 items.

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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:2, 255–260

Bibliographic databases:

UDC: 513.6
MSC: Primary 14K05; Secondary 14J99, 14H99
Received: 21.06.1974

Citation: Yu. G. Zarhin, “Endomorphisms of abelian varieties over fields of finite characteristic”, Izv. Akad. Nauk SSSR Ser. Mat., 39:2 (1975), 272–277; Math. USSR-Izv., 9:2 (1975), 255–260

Citation in format AMSBIB
\Bibitem{Zar75}
\by Yu.~G.~Zarhin
\paper Endomorphisms of abelian varieties over fields of finite characteristic
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 2
\pages 272--277
\mathnet{http://mi.mathnet.ru/izv1830}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=371897}
\zmath{https://zbmath.org/?q=an:0345.14014}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 2
\pages 255--260
\crossref{https://doi.org/10.1070/IM1975v009n02ABEH001476}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. G. Zarhin, “Weights of simple Lie algebras in the cohomology of algebraic varieties”, Math. USSR-Izv., 24:2 (1985), 245–281  mathnet  crossref  mathscinet  zmath
    2. Skorobogatov, AN, “FINITENESS THEOREM FOR THE BRAUER GROUP OF ABELIAN VARIETIES AND K3 SURFACES”, Journal of Algebraic Geometry, 17:3 (2008), 481  isi
    3. Yu.G.. Zarhin, “Abelian varieties over fields of finite characteristic”, centr.eur.j.math, 2014  crossref
    4. Marc Hindry, Amílcar Pacheco, “An analogue of the Brauer–Siegel theorem for abelian varieties in positive characteristic”, Mosc. Math. J., 16:1 (2016), 45–93  mathnet  mathscinet
    5. St. Petersburg Math. J., 29:1 (2018), 81–106  mathnet  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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