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 Mat. Zametki, 1977, Volume 22, Issue 1, Pages 3–11 (Mi mz8019)

Torsion of Abelian varieties of finite characteristic

Yu. G. Zarhin

Research computer Centre of USSR Academy of Sciences

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 $p>2$. 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.

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English version:
Mathematical Notes, 1977, 22:1, 493–498

Bibliographic databases:

UDC: 512

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
\Bibitem{Zar77} \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/mz8019} \mathscinet{http://www.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} 

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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
2. Yu. G. Zarhin, “Weights of simple Lie algebras in the cohomology of algebraic varieties”, Math. USSR-Izv., 24:2 (1985), 245–281
3. S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527–540
4. S. G. Tankeev, “K3 surfaces over number fields and $l$-adic representations”, Math. USSR-Izv., 33:3 (1989), 575–595
5. Izv. Math., 60:2 (1996), 379–389
6. Yu. G. Zarhin, “Very simple 2-adic representations and hyperelliptic Jacobians”, Mosc. Math. J., 2:2 (2002), 403–431
7. Yu. G. Zarhin, “Endomorphisms of Abelian varieties, cyclotomic extensions and Lie algebras”, Sb. Math., 201:12 (2010), 1801–1810
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