Comparisons of Lie algebra cohomologies of \((\varphi,\Gamma)\)-modules

We generalise a result of Fourquaux and Xie thereby completely determining the relationship between \(\mathbb{Q}_p\) and \(L\)-analytic Lie algebra cohomology of analytic \((\varphi_L,\Gamma_L)\)-modules. We use the results to conclude that for \(L\neq \mathbb{Q}_p,\) there exist examples of étale \...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Author: Steingart, Rustam
Format: Article
Language:English
Subjects:
Homology
Lie groups
Mathematical analysis
Modules
Rings (mathematics)
Online Access:Get full text
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Summary:We generalise a result of Fourquaux and Xie thereby completely determining the relationship between \(\mathbb{Q}_p\) and \(L\)-analytic Lie algebra cohomology of analytic \((\varphi_L,\Gamma_L)\)-modules. We use the results to conclude that for \(L\neq \mathbb{Q}_p,\) there exist examples of étale \((\varphi_L,\Gamma_L)\)-modules over Robba rings whose \(\mathbb{Q}_p\)-analytic cohomology does not arise as a base change of Galois cohomology.
ISSN:2331-8422