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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11302 |
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| _version_ | 1866908707185491968 |
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| author | Li, Xuanyou Liu, Chenhan |
| author_facet | Li, Xuanyou Liu, Chenhan |
| contents | We study the $p$-adic analogue of the $\ell$-adic hypergeometric sheaves for reductive groups, called the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules. They are overholonomic objects in the derived category of arithmetic $\mathscr{D}$-modules with Frobenius structures. Over the non-degenerate locus, the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules define $F$-isocrystals overconvergent along the complement of the non-degenerate locus. As an application, we use the theory of $L$-functions of overholonomic arithmetic $\mathscr{D}$-modules to study hypergeometric exponential sums on reductive groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $p$-adic hypergeometric $\mathscr{D}^{\dagger}(\infty)$-module and exponential sums on reductive groups Li, Xuanyou Liu, Chenhan Algebraic Geometry We study the $p$-adic analogue of the $\ell$-adic hypergeometric sheaves for reductive groups, called the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules. They are overholonomic objects in the derived category of arithmetic $\mathscr{D}$-modules with Frobenius structures. Over the non-degenerate locus, the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules define $F$-isocrystals overconvergent along the complement of the non-degenerate locus. As an application, we use the theory of $L$-functions of overholonomic arithmetic $\mathscr{D}$-modules to study hypergeometric exponential sums on reductive groups. |
| title | $p$-adic hypergeometric $\mathscr{D}^{\dagger}(\infty)$-module and exponential sums on reductive groups |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.11302 |