S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527

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Mathematics of the USSR-Izvestiya, 1988, Volume 31, Issue 3, Pages 527–540
DOI: https://doi.org/10.1070/IM1988v031n03ABEH001088 (Mi im1338)

This article is cited in 9 scientific papers (total in 9 papers)

Cycles on simple Abelian varieties of prime dimension over number fields

S. G. Tankeev

English version PDF (673 kB) Citations (9) Russian version article

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DOI: https://doi.org/10.1070/IM1988v031n03ABEH001088

Abstract: For all simple Abelian varieties of prime dimension over number fields the author proves 1) a version of the Mumford–Tate conjecture, asserting that the Lie algebra of the image of the

l

$l$ -adic representation is isomorphic to the Lie algebra of the set of

Q_{l}

$\mathbf Q_l$ -points of the Mumford–Tate group, and 2) the Tate conjecture on cycles.
Bibliography: 21 titles.

Received: 24.12.1985

Bibliographic databases:

UDC: 513.6

MSC: 14K15, 14C99

Language: English

Original paper language: Russian

Citation: S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527–540

Citation in format AMSBIB

\Bibitem{Tan87}

\by S.~G.~Tankeev

\paper Cycles on simple Abelian varieties of prime dimension over number fields

\jour Math. USSR-Izv.

\yr 1988

\vol 31

\issue 3

\pages 527--540

\mathnet{http://mi.mathnet.ru/eng/im1338}

\crossref{https://doi.org/10.1070/IM1988v031n03ABEH001088}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=933962}

\zmath{https://zbmath.org/?q=an:0681.14022|0656.14023}

Linking options:

https://www.mathnet.ru/eng/im1338

https://doi.org/10.1070/IM1988v031n03ABEH001088

https://www.mathnet.ru/eng/im/v51/i6/p1214

This publication is cited in the following 9 articles:

O. V. Oreshkina (Nikolskaya), “O gipotezakh Khodzha, Teita i Mamforda–Teita dlya rassloennykh proizvedenii semeistv regulyarnykh poverkhnostei s geometricheskim rodom 1”, Model. i analiz inform. sistem, 25:3 (2018), 312–322
Chun Yin Hui, Michael Larsen, “Type A images of Galois representations and maximality”, Math. Z., 284:3-4 (2016), 989
S. G. Tankeev, “On weights of the $l$ -adic representation and arithmetic of Frobenius eigenvalues”, Izv. Math., 63:1 (1999), 181–218
S. G. Tankeev, “On Frobenius traces”, Izv. Math., 62:1 (1998), 157–190
S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. Math., 60:2 (1996), 391–424
S. G. Tankeev, “Surfaces of type K3 over number fields and the Mumford–Tate conjecture. II”, Izv. Math., 59:3 (1995), 619–646
S. G. Tankeev, “Algebraic cycles on an abelian variety without complex multiplication”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 531–553
S. G. Tankeev, “Kuga–Satake abelian varieties and $l$ -adic representations”, Math. USSR-Izv., 39:1 (1992), 855–867
S. G. Tankeev, “K3 surfaces over number fields and the Mumford–Tate conjecture”, Math. USSR-Izv., 37:1 (1991), 191–208

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

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Abstract page:	427
Russian version PDF:	125
English version PDF:	27
References:	79
First page:	1

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