On the galois action on rational cohomology classes of type (p, p) of abelian varieties

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Abstract

TWe study the action of Gal(k/k) on the ring H* (A, Af), where A is an abelian variety defined over the field k of characteristic zero and Af is the ring of finite adèles of the field of rational numbers. We prove that there exists a subgroup of finite index in Gal(K/K) which acts as scalars on Rp(A)⊗Q Afwhere Rp(A)H2P ⫅(A, Q) is the space of rational cohomology classes of type (P, P).

Original languageEnglish
Pages (from-to)613-616
Number of pages4
JournalMathematics of the USSR - Sbornik
Volume23
Issue number4
DOIs
StatePublished - 30 Apr 1974

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