Yu. G. Zarhin, “Torsion of Abelian varieties of finite characteristic”, Mat. Zametki, 22:1 (1977), 3–11; Math. Notes, 22:1 (1977), 493

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Matematicheskie Zametki, 1977, Volume 22, Issue 1, Pages 3–11 (Mi mzm8019)

This article is cited in 13 scientific papers (total in 13 papers)

Torsion of Abelian varieties of finite characteristic

Yu. G. Zarhin

Research computer Centre of USSR Academy of Sciences

Full-text PDF (660 kB) Citations (13)

Abstract: The finiteness of the torsion of Abelian varieties with a complete real field of endomorphisms in the maximal Abelian extension of the field of definition is proven. This assertion is formally deduced from the finiteness hypothesis for isogenic Abelian varieties, proven for characteristic

p > 2

$p>2$ . The structure is studied of the Lie algebra of Galois groups acting in a Tate module; in particular, for fields of characteristic greater than two there is proven one-dimensionality of the center of the Lie algebra.

Received: 12.04.1976

English version:
Mathematical Notes, 1977, Volume 22, Issue 1, Pages 493–498
DOI: https://doi.org/10.1007/BF01147687

Bibliographic databases:

UDC: 512

Language: Russian

Citation: Yu. G. Zarhin, “Torsion of Abelian varieties of finite characteristic”, Mat. Zametki, 22:1 (1977), 3–11; Math. Notes, 22:1 (1977), 493–498

Citation in format AMSBIB

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\by Yu.~G.~Zarhin

\paper Torsion of Abelian varieties of finite characteristic

\jour Mat. Zametki

\yr 1977

\vol 22

\issue 1

\pages 3--11

\mathnet{http://mi.mathnet.ru/mzm8019}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=453757}

\zmath{https://zbmath.org/?q=an:0355.14018}

\transl

\jour Math. Notes

\yr 1977

\vol 22

\issue 1

\pages 493--498

\crossref{https://doi.org/10.1007/BF01147687}

Linking options:

https://www.mathnet.ru/eng/mzm8019

https://www.mathnet.ru/eng/mzm/v22/i1/p3

This publication is cited in the following 13 articles:

Yuri Zarhin, “Abelian varieties over fields of finite characteristic”, Open Mathematics, 12:5 (2014)
Marc Hindry, Nicolas Ratazzi, “Points de torsion sur les variétés abéliennes de type GSp”, J. Inst. Math. Jussieu, 11:1 (2012), 27
Anna Cadoret, Akio Tamagawa, “A uniform open image theorem for ℓ-adic representations, I”, Duke Math. J., 161:13 (2012)
Yu. G. Zarhin, “Endomorphisms of Abelian varieties, cyclotomic extensions and Lie algebras”, Sb. Math., 201:12 (2010), 1801–1810
Misha Gavrilovich, “A remark on transitivity of Galois action on the set of uniquely divisible abelian extensions in [graphic] ${\rm Ext}^1(E({\overline {{\mathbb {Q}}}}),\Lambda)$ ”, K-Theory, 38:2 (2008), 135
Yu. G. Zarhin, “Very simple 2-adic representations and hyperelliptic Jacobians”, Mosc. Math. J., 2:2 (2002), 403–431
Izv. Math., 60:2 (1996), 379–389
S. G. Tankeev, “K3 surfaces over number fields and $l$ -adic representations”, Math. USSR-Izv., 33:3 (1989), 575–595
S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527–540
Yu. G. Zarhin, “Endomorphisms and torsion of abelian varieties”, Duke Math. J., 54:1 (1987)
Yu. G. Zarhin, “Weights of simple Lie algebras in the cohomology of algebraic varieties”, Math. USSR-Izv., 24:2 (1985), 245–281
Yu. G. Zarhin, “Abelian varieties, $l$ -adic representations and $\mathrm{SL}_2$ ”, Math. USSR-Izv., 14:2 (1980), 275–288
Y. G. Zarhin, “Abelian varieties,l-adic representations and Lie algebras”, Invent Math, 55:2 (1979), 165

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

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