0 PEC(l) where G is a subgroup of finite index in Gt . /Z = 0, for the purpose of the following proof, it will be convenient to consider a more refined property of abelian groups, and to give it a name.

B) (CH)H

42 We also deduce that the differential is zero, and that the map coming from the spectral sequence is surjective. Going over to the direct limit of powers of a fixed prime l, we find that the map is also surjective. Deligne's theorem on the Weil conjectures implies that the group Hitd- 1 (X,QI/Z 1(d)) is finite ([CT/S/SJ, Theoreme 2, p. 780). We thus conclude that the group Hd- 2 (X, Jtd+l(Qt/Zt(d))) is finite. 2 a) below (in the trivial case i = d- 2) imply that Hd- 2 (X, Jtd+l(Qt/Zt( d))) is divisible.

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