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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 3, Pages 103–126 (Mi izv790)  

This article is cited in 3 scientific papers (total in 3 papers)

Algebraic cycles on an abelian variety without complex multiplication

S. G. Tankeev

Vladimir State University

Abstract: We prove a theorem to the effect that if a natural number $d$ is not exceptional, then all $d$-dimensional abelian varieties without complex multiplication satisfy the Grothendieck version of the general Hodge conjecture. Exceptional numbers have density zero in the set of natural numbers. If $\operatorname{End}(J)=\mathbf Z$, $J$ is defined over a number field, and $\dim J=2p$, where $p$ is a prime number, $p\ne 2$ and $p\ne 5$, then the Mumford–Tate conjecture and the Tate conjecture on algebraic cycles hold for the variety $J$.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:3, 531–553

Bibliographic databases:

UDC: 512.6
MSC: 14C30, 14K22, 32J25
Received: 25.04.1993

Citation: S. G. Tankeev, “Algebraic cycles on an abelian variety without complex multiplication”, Izv. RAN. Ser. Mat., 58:3 (1994), 103–126; Russian Acad. Sci. Izv. Math., 44:3 (1995), 531–553

Citation in format AMSBIB
\Bibitem{Tan94}
\by S.~G.~Tankeev
\paper Algebraic cycles on an abelian variety without complex multiplication
\jour Izv. RAN. Ser. Mat.
\yr 1994
\vol 58
\issue 3
\pages 103--126
\mathnet{http://mi.mathnet.ru/izv790}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1286841}
\zmath{https://zbmath.org/?q=an:0851.14005}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1995IzMat..44..531T}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 44
\issue 3
\pages 531--553
\crossref{https://doi.org/10.1070/IM1995v044n03ABEH001611}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RQ68000005}


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