Iwasawa cohomology of analytic $(φ_L,Γ_L)$-modules
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913562954301440 |
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| author | Steingart, Rustam |
| author_facet | Steingart, Rustam |
| contents | We show that the coadmissibility of the Iwasawa cohomology of an $L$-analytic Lubin-Tate $(φ_L,Γ_L)$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_02275 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Iwasawa cohomology of analytic $(φ_L,Γ_L)$-modules Steingart, Rustam Number Theory We show that the coadmissibility of the Iwasawa cohomology of an $L$-analytic Lubin-Tate $(φ_L,Γ_L)$-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. |
| title | Iwasawa cohomology of analytic $(φ_L,Γ_L)$-modules |
| topic | Number Theory |
| url | https://arxiv.org/abs/2212.02275 |