S. G. Tankeev, “K3 surfaces over number fields and $l$-adic representations”, Math. USSR-Izv., 33:3 (1989), 575

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Mathematics of the USSR-Izvestiya, 1989, Volume 33, Issue 3, Pages 575–595
DOI: https://doi.org/10.1070/IM1989v033n03ABEH000857 (Mi im1229)

This article is cited in 8 scientific papers (total in 8 papers)

K3 surfaces over number fields and

l

$l$ -adic representations

S. G. Tankeev

English version PDF (1012 kB) Citations (8) Russian version article

References:

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DOI: https://doi.org/10.1070/IM1989v033n03ABEH000857

Abstract: The Tate conjecture on algebraic cycles is proved for any algebraic K3 surface over a number field. If the canonical representation of the Hodge group in the

Q

$\mathbf Q$ -lattice of transcendental cohomology classes is absolutely irreducible, then the Mumford–Tate conjecture is true for such a K3 surface.
Bibliography: 18 titles.

Received: 14.04.1987

Bibliographic databases:

UDC: 513.6

MSC: Primary 14J28, 14G13, 11G35; Secondary 14G25, 14K15

Language: English

Original paper language: Russian

Citation: S. G. Tankeev, “K3 surfaces over number fields and

l

$l$ -adic representations”, Math. USSR-Izv., 33:3 (1989), 575–595

Citation in format AMSBIB

\Bibitem{Tan88}

\by S.~G.~Tankeev

\paper K3 surfaces over number fields and $l$-adic representations

\jour Math. USSR-Izv.

\yr 1989

\vol 33

\issue 3

\pages 575--595

\mathnet{http://mi.mathnet.ru/eng/im1229}

\crossref{https://doi.org/10.1070/IM1989v033n03ABEH000857}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=984218}

\zmath{https://zbmath.org/?q=an:0679.14019}

Linking options:

https://www.mathnet.ru/eng/im1229

https://doi.org/10.1070/IM1989v033n03ABEH000857

https://www.mathnet.ru/eng/im/v52/i6/p1252

This publication is cited in the following 8 articles:

Burt Totaro, “Recent progress on the Tate conjecture”, Bull. Amer. Math. Soc., 54:4 (2017), 575
S. G. Tankeev, “On the Brauer group of an arithmetic scheme. II”, Izv. Math., 67:5 (2003), 1007–1029
S. G. Tankeev, “On the Brauer group of an arithmetic scheme”, Izv. Math., 65:2 (2001), 357–388
S. G. Tankeev, “On the Brauer group”, Izv. Math., 64:4 (2000), 787–806
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, “Surfaces of type K3 over number fields and the Mumford–Tate conjecture. II”, Izv. Math., 59:3 (1995), 619–646
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

Известия Академии наук СССР. Серия математическая

Statistics & downloads:
Abstract page:	430
Russian version PDF:	114
English version PDF:	40
References:	80
First page:	1

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