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Mat. Sb. (N.S.), 1974, Volume 94(136), Number 4(8), Pages 649–652 (Mi msb3737)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Galois action on rational cohomology classes of type $(p,p)$ of Abelian varieties

M. V. Borovoi


Abstract: We study the action of $\operatorname{Gal}(\overline k/k)$ on the ring $H^*(A,\mathbf A^f)$, where $A$ is an Abelian variety defined over the field $k$ of characteristic zero and $\mathbf A^f$ is the ring of finite adèles of the field of rational numbers. We prove that there exists a subgroup of finite index in $\operatorname{Gal}(\overline k/k)$ which acts as scalars on $R^p(A)\otimes_{\mathbf Q}\mathbf A^f$, where $R^p(A)\subset H^{2p}(A,\mathbf Q)$ is the space of rational cohomology classes of type $(p,p)$.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:4, 613–616

Bibliographic databases:

UDC: 519.4+513.836
MSC: Primary 14K15, 14G13; Secondary 14G25, 14C30
Received: 24.10.1973

Citation: M. V. Borovoi, “On the Galois action on rational cohomology classes of type $(p,p)$ of Abelian varieties”, Mat. Sb. (N.S.), 94(136):4(8) (1974), 649–652; Math. USSR-Sb., 23:4 (1974), 613–616

Citation in format AMSBIB
\Bibitem{Bor74}
\by M.~V.~Borovoi
\paper On the Galois action on rational cohomology classes of type $(p,p)$ of Abelian varieties
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 4(8)
\pages 649--652
\mathnet{http://mi.mathnet.ru/msb3737}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=352101}
\zmath{https://zbmath.org/?q=an:0326.14013}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 4
\pages 613--616
\crossref{https://doi.org/10.1070/SM1974v023n04ABEH002185}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Borovoi, “Skhemy $M_C(G,h)$ i gruppa Mamforda–Teita”, UMN, 32:6(198) (1977), 245–246  mathnet  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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