On the de Rham flip-flopping in dual towers
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912954455162880 |
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| author | Dospinescu, Gabriel Nizioł, Wiesława |
| author_facet | Dospinescu, Gabriel Nizioł, Wiesława |
| contents | We prove a version of de Rham and Hyodo-Kato flip-flopping for dual towers of rigid analytic spaces including those coming from dual basic local Shimura varieties. The main tool are comparison theorems expressing the two cohomologies as pro-étale cohomology of corresponding relative period sheaves that, by definition, satisfy pro-étale descent. As an application, we show that de Rham and Hyodo-Kato cohomologies of finite level coverings of the Drinfeld space of any dimension $d$ over $K$ are admissible as representations of $\mathbb{GL}_{d+1}(K)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07869 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the de Rham flip-flopping in dual towers Dospinescu, Gabriel Nizioł, Wiesława Number Theory Algebraic Geometry We prove a version of de Rham and Hyodo-Kato flip-flopping for dual towers of rigid analytic spaces including those coming from dual basic local Shimura varieties. The main tool are comparison theorems expressing the two cohomologies as pro-étale cohomology of corresponding relative period sheaves that, by definition, satisfy pro-étale descent. As an application, we show that de Rham and Hyodo-Kato cohomologies of finite level coverings of the Drinfeld space of any dimension $d$ over $K$ are admissible as representations of $\mathbb{GL}_{d+1}(K)$. |
| title | On the de Rham flip-flopping in dual towers |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2603.07869 |