Finiteness of analytic cohomology of Lubin-Tate $(\varphi_L,\Gamma_L)$-modules

TL;DR

This paper establishes finiteness and base change properties for the analytic cohomology of families of $L$-analytic $(phi_L,Gamma_L)$-modules parametrized by affinoid algebras, using explicit Herr complexes.

Contribution

It proves finiteness and base change results for the analytic cohomology of Lubin-Tate $(phi_L,Gamma_L)$-modules, extending previous understanding in this area.

Findings

Finiteness of analytic cohomology established.

Base change properties proven for these modules.

Explicit description via Herr complexes provided.

Abstract

We prove finiteness and base change properties for analytic cohomology of families of $L$-analytic $(\varphi_L,\Gamma_L)$-modules parametrised by affinoid algebras in the sense of Tate. For technical reasons we work over a field $K$ containing a period of the Lubin-Tate group, which allows us to describe analytic cohomology in terms of an explicit generalized Herr complex.