Iwasawa cohomology of analytic $(\varphi_L,\Gamma_L)$-modules

TL;DR

This paper establishes a criterion linking the coadmissibility of Iwasawa cohomology of certain $(phi_L,Gamma_L)$-modules to the existence of a comparison isomorphism with their Lubin-Tate deformation's analytic cohomology, with implications for trianguline modules.

Contribution

It proves that coadmissibility is both necessary and sufficient for a comparison isomorphism, extending the understanding of analytic cohomology in the context of Lubin-Tate modules.

Findings

Coadmissibility is verified for trianguline modules.

Coadmissibility can be propagated to larger classes of modules.

The paper connects coadmissibility with the existence of comparison isomorphisms.

Abstract

We show that the coadmissibility of the Iwasawa cohomology of an $L$-analytic Lubin-Tate $(\varphi_L,\Gamma_L)$-module $M$ is necessary and sufficient for the existence of a comparison isomorphism between the former and the analytic cohomology of its Lubin-Tate deformation, which, roughly speaking, is given by the base change of $M$ to the algebra of $L$-analytic distributions. We verify that coadmissibility is satisfied in the trianguline case and show that it can be ``propagated'' to a reasonably large class of modules, provided it can be proven in the \'etale case.