Irregular Hodge filtration of hypergeometric differential equations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914105291440128 |
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| author | Qin, Yichen Xu, Daxin |
| author_facet | Qin, Yichen Xu, Daxin |
| contents | Fedorov and Sabbah--Yu calculated the (irregular) Hodge numbers of hypergeometric connections. In this paper, we study the irregular Hodge filtrations on hypergeometric connections defined by rational parameters, and provide a new proof of the aforementioned results. Our approach is based on a geometric interpretation of hypergeometric connections, which enables us to show that certain hypergeometric sums are everywhere ordinary on $|\mathbb{G}_{m,\mathbb{F}_p}|$ (i.e. "Frobenius Newton polygon equals to irregular Hodge polygon"). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05138 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Irregular Hodge filtration of hypergeometric differential equations Qin, Yichen Xu, Daxin Algebraic Geometry Number Theory Fedorov and Sabbah--Yu calculated the (irregular) Hodge numbers of hypergeometric connections. In this paper, we study the irregular Hodge filtrations on hypergeometric connections defined by rational parameters, and provide a new proof of the aforementioned results. Our approach is based on a geometric interpretation of hypergeometric connections, which enables us to show that certain hypergeometric sums are everywhere ordinary on $|\mathbb{G}_{m,\mathbb{F}_p}|$ (i.e. "Frobenius Newton polygon equals to irregular Hodge polygon"). |
| title | Irregular Hodge filtration of hypergeometric differential equations |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2308.05138 |