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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 6, Pages 1214–1227 (Mi izv1338)  

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

Cycles on simple Abelian varieties of prime dimension over number fields

S. G. Tankeev


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 $l$-adic representation is isomorphic to the Lie algebra of the set of $\mathbf Q_l$-points of the Mumford–Tate group, and 2) the Tate conjecture on cycles.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:3, 527–540

Bibliographic databases:

UDC: 513.6
MSC: 14K15, 14C99
Received: 24.12.1985

Citation: S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1214–1227; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 6
\pages 1214--1227
\mathnet{http://mi.mathnet.ru/izv1338}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=933962}
\zmath{https://zbmath.org/?q=an:0681.14022|0656.14023}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 3
\pages 527--540
\crossref{https://doi.org/10.1070/IM1988v031n03ABEH001088}


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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, “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
    4. 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
    5. S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. Math., 60:2 (1996), 391–424  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. S. G. Tankeev, “On Frobenius traces”, Izv. Math., 62:1 (1998), 157–190  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. 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
    8. 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  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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