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Monday, October 15, 2018

**Abstract:** In this talk, I’ll explain the relation between congruence and (continuous) group cohomology of $\mathbb{Z}_p^\times$-representations in invertible $\mathbb{Z}_p$-modules. The first half of the talk will focus on explicit computations of the two sides (including the $p=2$ case). In the second half, the connection between congruence and group cohomology will be built using the chromatic resolution (Cousin complex) of the $\mathbb{Z}_p^\times$-representations. The discussion here also applies to open subgroups of $\mathbb{Z}_p^\times$.