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

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Matematicheskie Zametki, 1976, Volume 19, Issue 3, Pages 393–400 (Mi mzm7758)

This article is cited in 10 scientific papers (total in 10 papers)

Abelian varieties in characteristic $p$

Yu. G. Zarhin

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

Full-text PDF (505 kB) Citations (10)

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.

Received: 30.06.1975

English version:
Mathematical Notes, 1976, Volume 19, Issue 3, Pages 240–244
DOI: https://doi.org/10.1007/BF01437858

Bibliographic databases:

UDC: 512

Language: Russian

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/mzm7758}

\mathscinet{http://mathscinet.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}

Linking options:

https://www.mathnet.ru/eng/mzm7758

https://www.mathnet.ru/eng/mzm/v19/i3/p393

This publication is cited in the following 10 articles:

Yanshuai Qin, “On the Brauer groups of fibrations”, Math. Z., 307:1 (2024)
St. Petersburg Math. J., 29:1 (2018), 81–106
Alexei N. Skorobogatov, Yuri G. Zarhin, “A Finiteness Theorem for the Brauer Group of K3 Surfaces in Odd Characteristic”, Int Math Res Notices, 2015:21 (2015), 11404
Yuri Zarhin, “Abelian varieties over fields of finite characteristic”, Open Mathematics, 12:5 (2014)
Nicolas Stalder, “The semisimplicity conjecture for A-motives”, Compositio Math., 146:3 (2010), 561
Skorobogatov, AN, “FINITENESS THEOREM FOR THE BRAUER GROUP OF ABELIAN VARIETIES AND K3 SURFACES”, Journal of Algebraic Geometry, 17:3 (2008), 481
Yu. G. Zarhin, “Very simple 2-adic representations and hyperelliptic Jacobians”, Mosc. Math. J., 2:2 (2002), 403–431
A. Silverberg, Séminaire de Théorie des Nombres, Paris, 1990–91, 1993, 221
S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”, Math. USSR-Izv., 18:2 (1982), 349–380
Yu. G. Zarhin, “Abelian varieties, $l$-adic representations and $\mathrm{SL}_2$”, Math. USSR-Izv., 14:2 (1980), 275–288

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

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