Duality and local group cohomology

Hewitt, P.

doi:10.1090/S0002-9939-98-04543-2

Duality and local group cohomology
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by P. R. Hewitt PDF

Proc. Amer. Math. Soc. 126 (1998), 1909-1914 Request permission

Abstract:

Let $G$ be a group, let $k$ be a field, and let ${\mathcal {L}}$ be a local system — an upwardly directed collection of subgroups whose union is $G$. In this paper we give a short, elementary proof of the following result: If either $A$ is a $k$-$kG$-bimodule, or else $k$ is finite dimensional over its center, then $\operatorname {Ext}^{*}_{G}(A,B^{\vee }) =\varprojlim _{L\in \mathcal {L}} \operatorname {Ext}^{*}_{L}(A,B^{\vee })$. From this we deduce as easy corollaries some recent results of Meierfrankenfeld and Wehrfritz on the cohomology of a finitary module.

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