TY - JOUR
T1 - On the galois action on rational cohomology classes of type (p, p) of abelian varieties
AU - BorovoǏ, M. V.
PY - 1974/4/30
Y1 - 1974/4/30
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=0000839424&partnerID=8YFLogxK
U2 - 10.1070/SM1974v023n04ABEH002185
DO - 10.1070/SM1974v023n04ABEH002185
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AN - SCOPUS:0000839424
SN - 0025-5734
VL - 23
SP - 613
EP - 616
JO - Mathematics of the USSR - Sbornik
JF - Mathematics of the USSR - Sbornik
IS - 4
ER -