Computing Crystalline Cohomology and p-Divisible Groups for Curves over Finite Fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918296918425600 |
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| author | Booher, Jeremy |
| author_facet | Booher, Jeremy |
| contents | Let $X$ be a smooth projective curve over a finite field of characteristic $p$. We describe and implement a practical algorithm for computing the $p$-divisible group $Jac(X)[p^\infty]$ via computing its Dieudonné module, or equivalently computing the Frobenius and Verschiebung operators on the first crystalline cohomology of $X$. We build on Tuitman's $p$-adic point counting algorithm, which computes the rigid cohomology of $X$ and requires a ``nice'' lift of $X$ to be provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14006 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing Crystalline Cohomology and p-Divisible Groups for Curves over Finite Fields Booher, Jeremy Number Theory Algebraic Geometry Let $X$ be a smooth projective curve over a finite field of characteristic $p$. We describe and implement a practical algorithm for computing the $p$-divisible group $Jac(X)[p^\infty]$ via computing its Dieudonné module, or equivalently computing the Frobenius and Verschiebung operators on the first crystalline cohomology of $X$. We build on Tuitman's $p$-adic point counting algorithm, which computes the rigid cohomology of $X$ and requires a ``nice'' lift of $X$ to be provided. |
| title | Computing Crystalline Cohomology and p-Divisible Groups for Curves over Finite Fields |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2601.14006 |