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.
\Bibitem{Tan82}
\by S.~G.~Tankeev
\paper Cycles on simple Abelian varieties of prime dimension
\jour Math. USSR-Izv.
\yr 1983
\vol 20
\issue 1
\pages 157--171
\mathnet{http://mi.mathnet.ru/eng/im1611}
\crossref{https://doi.org/10.1070/IM1983v020n01ABEH001345}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=643899}
\zmath{https://zbmath.org/?q=an:0587.14005}
Linking options:
https://www.mathnet.ru/eng/im1611
https://doi.org/10.1070/IM1983v020n01ABEH001345
https://www.mathnet.ru/eng/im/v46/i1/p155
This publication is cited in the following 16 articles:
S. G. Tankeev, “On the standard conjecture for a fourfold with
$1$-parameter fibration by Abelian varieties”, Izv. Math., 88:2 (2024), 339–368
O. V. Makarova, “Invariant Cycles on Abelian Schemes”, J Math Sci, 250:1 (2020), 69
Ayal Sharon, “Propositional Logic Applied to Three Contradictory Definitions of the Zeta Function”, SSRN Journal, 2019
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
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
S. G. Tankeev, “On algebraic cycles on complex Abelian schemes over smooth projective curves”, Izv. Math., 72:4 (2008), 817–844
S. G. Tankeev, “Monoidal transformations and conjectures on algebraic cycles”, Izv. Math., 71:3 (2007), 629–655
S. G. Tankeev, “On the standard conjecture for complex Abelian schemes over smooth projective curves”, Izv. Math., 67:3 (2003), 597–635
S. Abdulali, “Hodge structures on abelian varieties of CM-type”, crll, 2001:534 (2001), 33
S. G. Tankeev, “On weights of the $l$-adic representation and arithmetic of Frobenius eigenvalues”, Izv. Math., 63:1 (1999), 181–218
S. G. Tankeev, “Cycles of small codimension on a simple $2p$- or $4p$-dimensional Abelian variety”, Izv. Math., 63:6 (1999), 1221–1262
S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. Math., 60:2 (1996), 391–424
S. G. Tankeev, “Abelian varieties and the general Hodge conjecture”, Russian Acad. Sci. Izv. Math., 43:1 (1994), 179–191
Wenchen Chi, “On the l-adic representations attached to simple abelian varieties of type IV”, BAZ, 44:1 (1991), 71
S. G. Tankeev, “Cycles on simple Abelian varieties of prime dimension over number fields”, Math. USSR-Izv., 31:3 (1988), 527–540
S. G. Tankeev, “On cycles on Abelian varieties of prime dimension over finite or number fields”, Math. USSR-Izv., 22:2 (1984), 329–337
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