Continuous group cohomology with coefficients in locally analytic vectors of admissible ℚ_p -Banach space representations

2023/02/16 by Fust, Paulina
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2302.08369

Abstract

We show that the continuous cohomology groups of a p -adic reductive group with coefficients in the locally analytic vectors of an admissible ℚ_p -Banach space representation are homeomorphic to those with coefficients in the Banach space representation itself. Moreover, we deduce that the canonical topologies on those continuous cohomology groups are Hausdorff and are the uniquely determined finest locally convex topologies.

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