Comparisons of Lie algebra cohomologies of $(φ,Γ)$-modules
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910911240863744 |
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| author | Steingart, Rustam |
| author_facet | Steingart, Rustam |
| contents | 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 $(φ_L,Γ_L)$-modules. We use the results to conclude that for $L\neq \mathbb{Q}_p,$ there exist examples of étale $(φ_L,Γ_L)$-modules over Robba rings whose $\mathbb{Q}_p$-analytic cohomology does not arise as a base change of Galois cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07799 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comparisons of Lie algebra cohomologies of $(φ,Γ)$-modules Steingart, Rustam Number Theory 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 $(φ_L,Γ_L)$-modules. We use the results to conclude that for $L\neq \mathbb{Q}_p,$ there exist examples of étale $(φ_L,Γ_L)$-modules over Robba rings whose $\mathbb{Q}_p$-analytic cohomology does not arise as a base change of Galois cohomology. |
| title | Comparisons of Lie algebra cohomologies of $(φ,Γ)$-modules |
| topic | Number Theory |
| url | https://arxiv.org/abs/2311.07799 |