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arXiv · 2212.02275

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

Rustam Steingart
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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.

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Rustam Steingart. 2022-12-05. Iwasawa cohomology of analytic $(\varphi_L,\Gamma_L)$-modules. https://doi.org/10.4064/aa230512-1-7

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