On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914092066799616 |
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| author | Steingart, Rustam |
| author_facet | Steingart, Rustam |
| contents | Let $K/E/\mathbb{Q}_p$ be a tower of finite extensions with $E$ Galois. We relate the category of $G_K$-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in $E$ with $E$-$G_K$-$B$-pairs and describe crystalline and de Rham objects in explicit terms. When $E$ is a proper extension, we give a new description of the category in terms of compatible tuples of $\mathbf{B}_e$-modules, which allows us to compute Galois cohomology in terms of an explicit Čech complex which can serve as a replacement of the fundamental exact sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension Steingart, Rustam Number Theory Algebraic Geometry Let $K/E/\mathbb{Q}_p$ be a tower of finite extensions with $E$ Galois. We relate the category of $G_K$-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in $E$ with $E$-$G_K$-$B$-pairs and describe crystalline and de Rham objects in explicit terms. When $E$ is a proper extension, we give a new description of the category in terms of compatible tuples of $\mathbf{B}_e$-modules, which allows us to compute Galois cohomology in terms of an explicit Čech complex which can serve as a replacement of the fundamental exact sequence. |
| title | On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2510.12533 |