Continuous Cohomology and Homology of Profinite Groups

We develop cohomological and homological theories for a profinite group $G$ with coefficients in the Pontryagin dual categories of pro-discrete and ind-profinite $G$-modules, respectively. The standard results of group (co)homology hold for this theory: we prove versions of the Universal Coefficient Theorem, the Lyndon-Hochschild-Serre spectral sequence and Shapiro's Lemma.

2010 Mathematics Subject Classification: Primary 20J06; Secondary 20E18, 20J05, 13J10.

Keywords and Phrases: Continuous cohomology, profinite groups, quasi-abelian categories.

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