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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 4, Pages 877–889 (Mi izv992)  

This article is cited in 2 scientific papers (total in 2 papers)

Kuga–Satake abelian varieties and $l$-adic representations

S. G. Tankeev

Vladimir Polytechnical Institute

Abstract: Let $J$ be a Kuga–Satake abelian variety defined over a number field $k\hookrightarrow\mathbf C$. Assuming a certain arithmetic condition on the canonical field $K$ associated to $J\otimes_k\mathbf C$, we prove the Mumford–Tate conjecture concerning the Lie algebra of the image of the $l$-adic representation in the one-dimensional cohomology of $J$.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:1, 855–867

Bibliographic databases:

UDC: 513.6
MSC: Primary 11G10, 14K15; Secondary 14G25
Received: 19.06.1990

Citation: S. G. Tankeev, “Kuga–Satake abelian varieties and $l$-adic representations”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991), 877–889; Math. USSR-Izv., 39:1 (1992), 855–867

Citation in format AMSBIB
\Bibitem{Tan91}
\by S.~G.~Tankeev
\paper Kuga--Satake abelian varieties and $l$-adic representations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 4
\pages 877--889
\mathnet{http://mi.mathnet.ru/izv992}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1137590}
\zmath{https://zbmath.org/?q=an:0791.14020}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..39..855T}
\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 39
\issue 1
\pages 855--867
\crossref{https://doi.org/10.1070/IM1992v039n01ABEH002229}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992JQ84600008}


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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, “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
    2. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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