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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 1, Pages 155–170 (Mi izv1611)  

This article is cited in 13 scientific papers (total in 13 papers)

Cycles on simple Abelian varieties of prime dimension

S. G. Tankeev


Abstract: The Hodge conjecture on algebraic cycles is proved for all simple Abelian varieties of prime dimension over the field of complex numbers.
Bibliography: 10 titles.

Full text: PDF file (1220 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1983, 20:1, 157–171

Bibliographic databases:

UDC: 513.6
MSC: Primary 14C30, 14K20; Secondary 14F25, 32J25, 14C10, 14C20, 14K22
Received: 10.09.1981

Citation: S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension”, Izv. Akad. Nauk SSSR Ser. Mat., 46:1 (1982), 155–170; Math. USSR-Izv., 20:1 (1983), 157–171

Citation in format AMSBIB
\Bibitem{Tan82}
\by S.~G.~Tankeev
\paper Cycles on simple Abelian varieties of prime dimension
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 1
\pages 155--170
\mathnet{http://mi.mathnet.ru/izv1611}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=643899}
\zmath{https://zbmath.org/?q=an:0587.14005}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 1
\pages 157--171
\crossref{https://doi.org/10.1070/IM1983v020n01ABEH001345}


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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, “On cycles on Abelian varieties of prime dimension over finite or number fields”, Math. USSR-Izv., 22:2 (1984), 329–337  mathnet  crossref  mathscinet  zmath
    2. S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527–540  mathnet  crossref  mathscinet  zmath
    3. Wenchen Chi, “On the l-adic representations attached to simple abelian varieties of type IV”, BAZ, 44:1 (1991), 71  crossref
    4. S. G. Tankeev, “Abelian varieties and the general Hodge conjecture”, Russian Acad. Sci. Izv. Math., 43:1 (1994), 179–191  mathnet  crossref  mathscinet  zmath  adsnasa  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 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
    7. S. G. Tankeev, “Cycles of small codimension on a simple $2p$- or $4p$-dimensional Abelian variety”, Izv. Math., 63:6 (1999), 1221–1262  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. S. Abdulali, “Hodge structures on abelian varieties of CM-type”, crll, 2001:534 (2001), 33  crossref  mathscinet  zmath
    9. S. G. Tankeev, “On the standard conjecture for complex Abelian schemes over smooth projective curves”, Izv. Math., 67:3 (2003), 597–635  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. S. G. Tankeev, “Monoidal transformations and conjectures on algebraic cycles”, Izv. Math., 71:3 (2007), 629–655  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. S. G. Tankeev, “On algebraic cycles on complex Abelian schemes over smooth projective curves”, Izv. Math., 72:4 (2008), 817–844  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. O. V. Nikolskaya, “Ob algebraicheskikh tsiklakh na rassloennykh proizvedeniyakh neizotrivialnykh semeistv regulyarnykh poverkhnostei s geometricheskim rodom 1”, Model. i analiz inform. sistem, 23:4 (2016), 440–465  mathnet  crossref  mathscinet  elib
    13. 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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