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Mat. Zametki, 1976, Volume 19, Issue 3, Pages 393–400 (Mi mz7758)  

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

Abelian varieties in characteristic $p$

Yu. G. Zarhin

Scientific-Research Computing Center, Academy of Sciences of the USSR,

Abstract: In this paper Tate's finiteness conjecture for isogenies of polarized Abelian varieties in characteristic $p>2$ is proved. From this conjecture it is deduced that Tate modules are semisimple and that Tate's conjecture on the homomorphisms of Abelian varieties is valid.

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English version:
Mathematical Notes, 1976, 19:3, 240–244

Bibliographic databases:

UDC: 512
Received: 30.06.1975

Citation: Yu. G. Zarhin, “Abelian varieties in characteristic $p$”, Mat. Zametki, 19:3 (1976), 393–400; Math. Notes, 19:3 (1976), 240–244

Citation in format AMSBIB
\Bibitem{Zar76}
\by Yu.~G.~Zarhin
\paper Abelian varieties in characteristic $p$
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 3
\pages 393--400
\mathnet{http://mi.mathnet.ru/mz7758}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=422287}
\zmath{https://zbmath.org/?q=an:0342.14011}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 3
\pages 240--244
\crossref{https://doi.org/10.1007/BF01437858}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. G. Zarhin, “Abelian varieties, $l$-adic representations and $\mathrm{SL}_2$”, Math. USSR-Izv., 14:2 (1980), 275–288  mathnet  crossref  mathscinet  zmath  isi
    2. S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”, Math. USSR-Izv., 18:2 (1982), 349–380  mathnet  crossref  mathscinet  zmath
    3. Yu. G. Zarhin, “Very simple 2-adic representations and hyperelliptic Jacobians”, Mosc. Math. J., 2:2 (2002), 403–431  mathnet  crossref  mathscinet  zmath  elib
    4. Skorobogatov, AN, “FINITENESS THEOREM FOR THE BRAUER GROUP OF ABELIAN VARIETIES AND K3 SURFACES”, Journal of Algebraic Geometry, 17:3 (2008), 481  isi
    5. St. Petersburg Math. J., 29:1 (2018), 81–106  mathnet  crossref  mathscinet  isi  elib
  • Математические заметки Mathematical Notes
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