On an analytic version of Lazard's isomorphism

TL;DR

This paper establishes a comparison theorem linking locally analytic group cohomology with Lie algebra cohomology for nonarchimedean Lie groups, providing a simplified proof akin to van-Est's isomorphism.

Contribution

It introduces an analytic version of Lazard's isomorphism, connecting group and Lie algebra cohomology in a nonarchimedean setting with minimal functional analysis.

Findings

Proves a comparison theorem between group and Lie algebra cohomology.

Provides a simplified proof similar to van-Est's isomorphism.

Establishes foundational results for nonarchimedean analytic groups.

Abstract

We prove a comparison theorem between locally analytic group cohomology and Lie algebra cohomology for locally analytic representations of a Lie group over a nonarchimedean field of characteristic 0. The proof is similar to that of van-Est's isomorphism and uses only a minimum of functional analysis.