Continuous cohomology and homology of profinite groups
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.