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Mathematics of the USSR-Sbornik, 1971, Volume 14, Issue 4, Pages 615–624
DOI: https://doi.org/10.1070/SM1971v014n04ABEH002824 (Mi sm3281) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Interrelations between the Tate and Hodge conjectures for Abelian varieties

I. I. Pyatetskii-Shapiro
English version PDF (716 kB) Citations (14) Russian version article
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DOI: https://doi.org/10.1070/SM1971v014n04ABEH002824
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.
Received: 05.04.1971
Bibliographic databases:
UDC: 519.4+513.836
MSC: Primary 14K05; Secondary 10D25
Language: English
Original paper language: Russian
Citation: I. I. Pyatetskii-Shapiro, “Interrelations between the Tate and Hodge conjectures for Abelian varieties”, 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 Math. USSR-Sb.
\yr 1971
\vol 14
\issue 4
\pages 615--624
\mathnet{http://mi.mathnet.ru//eng/sm3281}
\crossref{https://doi.org/10.1070/SM1971v014n04ABEH002824}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=294352}
\zmath{https://zbmath.org/?q=an:0229.14014}
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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