The cohomology of locally analytic representations

Abstract

We develop a cohomology theory for locally analytic representations of p -adic Lie groups on nonarchimedean locally convex vector spaces. There are versions of Pontrjagin duality, Shapiro's lemma and a Hochschild-Serre spectral sequence. As an application, we give the definition of a supercuspidal locally analytic representation of a p -adic reductive group and study extensions between locally analytic principal series representations.