Continuous cohomology and homology of profinite groups (Q504291)

Summary: 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.