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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 6, Pages 1252–1271 (Mi izv1229)  

This article is cited in 7 scientific papers (total in 7 papers)

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

S. G. Tankeev


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

Full text: PDF file (2114 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:3, 575–595

Bibliographic databases:

UDC: 513.6
MSC: Primary 14J28, 14G13, 11G35; Secondary 14G25, 14K15
Received: 14.04.1987

Citation: S. G. Tankeev, “K3 surfaces over number fields and $l$-adic representations”, Izv. Akad. Nauk SSSR Ser. Mat., 52:6 (1988), 1252–1271; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 6
\pages 1252--1271
\mathnet{http://mi.mathnet.ru/izv1229}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=984218}
\zmath{https://zbmath.org/?q=an:0679.14019}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 3
\pages 575--595
\crossref{https://doi.org/10.1070/IM1989v033n03ABEH000857}


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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, “K3 surfaces over number fields and the Mumford–Tate conjecture”, Math. USSR-Izv., 37:1 (1991), 191–208  mathnet  crossref  mathscinet  zmath  adsnasa
    2. S. G. Tankeev, “Kuga–Satake abelian varieties and $l$-adic representations”, Math. USSR-Izv., 39:1 (1992), 855–867  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. 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
    4. 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
    5. S. G. Tankeev, “On the Brauer group”, Izv. Math., 64:4 (2000), 787–806  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. S. G. Tankeev, “On the Brauer group of an arithmetic scheme”, Izv. Math., 65:2 (2001), 357–388  mathnet  crossref  crossref  mathscinet  zmath  elib
    7. S. G. Tankeev, “On the Brauer group of an arithmetic scheme. II”, Izv. Math., 67:5 (2003), 1007–1029  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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