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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 2, Pages 294–308 (Mi izv1684)  

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

Abelian varieties, $l$-adic representations and $\mathrm{SL}_2$

Yu. G. Zarhin


Abstract: In this article the Lie algebra of a Galois group which operates on the Tate module of a two- or three-dimensional Abelian variety is calculated. It is assumed that the Abelian variety does not have nontrivial endomorphisms and is defined over a global field with characteristic greater than two.
Bibliography: 14 titles.

Full text: PDF file (1175 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1980, 14:2, 275–288

Bibliographic databases:

UDC: 513.6
MSC: Primary 14K05; Secondary 22E60
Received: 19.06.1978

Citation: Yu. G. Zarhin, “Abelian varieties, $l$-adic representations and $\mathrm{SL}_2$”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 294–308; Math. USSR-Izv., 14:2 (1980), 275–288

Citation in format AMSBIB
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\by Yu.~G.~Zarhin
\paper Abelian varieties, $l$-adic representations and~$\mathrm{SL}_2$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 2
\pages 294--308
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=534595}
\zmath{https://zbmath.org/?q=an:0451.14015|0433.14031}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 14
\issue 2
\pages 275--288
\crossref{https://doi.org/10.1070/IM1980v014n02ABEH001105}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980KM96800004}


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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. S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”, Math. USSR-Izv., 18:2 (1982), 349–380  mathnet  crossref  mathscinet  zmath
    2. Yu. G. Zarhin, “Cohomologies of algebraic manifolds and representations of semisimple Lie algebras”, Funct. Anal. Appl., 15:4 (1981), 295–297  mathnet  crossref  mathscinet  zmath  isi
    3. 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
    4. S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527–540  mathnet  crossref  mathscinet  zmath
    5. S. G. Tankeev, “K3 surfaces over number fields and $l$-adic representations”, Math. USSR-Izv., 33:3 (1989), 575–595  mathnet  crossref  mathscinet  zmath
    6. Yuri Zarhin, “Torsion of Abelian varieties over GL(2)-extensions of number fields”, Math Ann, 284:4 (1989), 631  crossref  mathscinet  zmath  isi  elib
    7. Yu. G. Zarhin, “Torsion and endomorphisms of Abelian varieties over infinite extensions of number fields”, Math. USSR-Izv., 38:3 (1992), 647–657  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. S. G. Tankeev, “Algebraic cycles on an abelian variety without complex multiplication”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 531–553  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. S. G. Tankeev, “Surfaces of type K3 over number fields and the Mumford–Tate conjecture. II”, Izv. Math., 59:3 (1995), 619–646  mathnet  crossref  mathscinet  zmath  isi
    10. S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. Math., 60:2 (1996), 391–424  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. S. G. Tankeev, “On weights of the $l$-adic representation and arithmetic of Frobenius eigenvalues”, Izv. Math., 63:1 (1999), 181–218  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Yu. G. Zarhin, “Very simple 2-adic representations and hyperelliptic Jacobians”, Mosc. Math. J., 2:2 (2002), 403–431  mathnet  crossref  mathscinet  zmath  elib
    13. Yu.G.. Zarhin, “Eigenvalues of Frobenius endomorphisms of abelian varieties of low dimension”, Journal of Pure and Applied Algebra, 2014  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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