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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Published in:arXiv.org 2024-10
Main Author: Steingart, Rustam
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Homology
Isomorphism
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description 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.
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subjects Homology
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Modules
title Iwasawa cohomology of analytic \((\varphi_L,\Gamma_L)\)-modules
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