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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2404.16291 |
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| _version_ | 1866911852813877248 |
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| author | Ohkubo, Shun |
| author_facet | Ohkubo, Shun |
| contents | Let $K$ be a complete non-archimedean valuation field of characteristic $0$, with non-trivial valuation, equipped with (possibly multiple) commuting bounded derivations. We prove a decomposition theorem for finite differential modules over $K$, where decompositions regarding the extrinsic subsidiary $\partial$-generic radii of convergence in the sense of Kedlaya-Xiao. Our result is a refinement of a previous decomposition theorem due to Kedlaya and Xiao. As a key step in the proof, we prove a decomposition theorem in a stronger form in the case where $K$ is equipped with a single derivation. To achieve this goal, we construct an object $f_{0*}L_0$ representing the usual dual functor and study some filtrations of $f_{0*}L_0$, which is used to construct the direct summands appearing in our decomposition theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality for differential modules over complete non-archimedean valuation field of characteristic zero Ohkubo, Shun Number Theory Let $K$ be a complete non-archimedean valuation field of characteristic $0$, with non-trivial valuation, equipped with (possibly multiple) commuting bounded derivations. We prove a decomposition theorem for finite differential modules over $K$, where decompositions regarding the extrinsic subsidiary $\partial$-generic radii of convergence in the sense of Kedlaya-Xiao. Our result is a refinement of a previous decomposition theorem due to Kedlaya and Xiao. As a key step in the proof, we prove a decomposition theorem in a stronger form in the case where $K$ is equipped with a single derivation. To achieve this goal, we construct an object $f_{0*}L_0$ representing the usual dual functor and study some filtrations of $f_{0*}L_0$, which is used to construct the direct summands appearing in our decomposition theorem. |
| title | Duality for differential modules over complete non-archimedean valuation field of characteristic zero |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.16291 |