Continuous cohomology and homology of profinite groups

2003/06/26 by Boggi, Marco, Cook, Ged Corob
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0306381

Abstract

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.

Related

• Pontryagin duality and sheaves of profinite modules
• Solid Duality for Profinite Groups
• Relative cohomology theory for profinite groups
• A homotopy orbit spectrum for profinite groups
• Relative extensions and cohomology of profinite groups