Iwasawa cohomology of analytic $({\phi }_L,{\Gamma }_L)$-modules

Abstract

We show that the coadmissibility of the Iwasawa cohomology of an $L$-analytic Lubin-Tate $({\phi }_L,{\Gamma }_L)$-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.

arXiv commentupdated, published version

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