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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 4(8), Pages 610–620 (Mi msb3281)  

This article is cited in 11 scientific papers (total in 11 papers)

Interrelations between the Tate and Hodge conjectures for Abelian varieties

I. I. Pyatetskii-Shapiro


Abstract: In the paper the action of the Galois group $G(\overline k\mid k)$ on $H_l^m(A)$ is investigated, where $A$ is an Abelian variety defined over a field $k$ of characteristic zero. We prove that the Galois group acts on the rational cohomology classes of type $(p,p)$ as far as they are algebraic.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:4, 615–624

Bibliographic databases:

UDC: 519.4+513.836
MSC: Primary 14K05; Secondary 10D25
Received: 05.04.1971

Citation: I. I. Pyatetskii-Shapiro, “Interrelations between the Tate and Hodge conjectures for Abelian varieties”, Mat. Sb. (N.S.), 85(127):4(8) (1971), 610–620; Math. USSR-Sb., 14:4 (1971), 615–624

Citation in format AMSBIB
\Bibitem{Pya71}
\by I.~I.~Pyatetskii-Shapiro
\paper Interrelations between the Tate and Hodge conjectures for Abelian varieties
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 4(8)
\pages 610--620
\mathnet{http://mi.mathnet.ru/msb3281}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=294352}
\zmath{https://zbmath.org/?q=an:0229.14014}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 4
\pages 615--624
\crossref{https://doi.org/10.1070/SM1971v014n04ABEH002824}


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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. M. V. Borovoi, “On the Galois action on rational cohomology classes of type $(p,p)$ of Abelian varieties”, Math. USSR-Sb., 23:4 (1974), 613–616  mathnet  crossref  mathscinet  zmath
    2. M. V. Borovoi, “Skhemy $M_C(G,h)$ i gruppa Mamforda–Teita”, UMN, 32:6(198) (1977), 245–246  mathnet  mathscinet  zmath
    3. S. G. Tankeev, “On algebraic cycles on Abelian varieties”, Math. USSR-Izv., 12:3 (1978), 617–643  mathnet  crossref  mathscinet  zmath
    4. S. G. Tankeev, “On algebraic cycles on surfaces and Abelian varieties”, Math. USSR-Izv., 18:2 (1982), 349–380  mathnet  crossref  mathscinet  zmath
    5. S. G. Tankeev, “On algebraic cycles on simple 5-dimensional Abelian varieties”, Math. USSR-Izv., 19:1 (1982), 95–123  mathnet  crossref  mathscinet  zmath
    6. 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
    7. 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
    8. S. G. Tankeev, “K3 surfaces over number fields and $l$-adic representations”, Math. USSR-Izv., 33:3 (1989), 575–595  mathnet  crossref  mathscinet  zmath
    9. 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
    10. S. G. Tankeev, “Cycles on Abelian varieties and exceptional numbers”, Izv. Math., 60:2 (1996), 391–424  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. S. G. Tankeev, “On Frobenius traces”, Izv. Math., 62:1 (1998), 157–190  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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