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

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 spea...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Author: Steingart, Rustam
Format: Article
Language:English
Subjects:
Homology
Isomorphism
Mathematical analysis
Modules
Online Access:Get full text
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Summary: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 étale case.
ISSN:2331-8422
DOI:10.48550/arxiv.2212.02275