Tame torsion and the tame inverse Galois problem
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866908757426962432 |
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| author | Bisatt, Matthew Dokchitser, Tim |
| author_facet | Bisatt, Matthew Dokchitser, Tim |
| contents | Fix a positive integer $g$ and a squarefree integer $m$. We prove the existence of a genus $g$ curve $C/\mathbb{Q}$ such that the mod $m$ representation of its Jacobian is tame. The method is to analyse the period matrices of hyperelliptic Mumford curves, which could be of independent interest. As an application, we study the tame version of the inverse Galois problem for symplectic matrix groups over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_08043 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Tame torsion and the tame inverse Galois problem Bisatt, Matthew Dokchitser, Tim Number Theory 11G30, 14G22 Fix a positive integer $g$ and a squarefree integer $m$. We prove the existence of a genus $g$ curve $C/\mathbb{Q}$ such that the mod $m$ representation of its Jacobian is tame. The method is to analyse the period matrices of hyperelliptic Mumford curves, which could be of independent interest. As an application, we study the tame version of the inverse Galois problem for symplectic matrix groups over finite fields. |
| title | Tame torsion and the tame inverse Galois problem |
| topic | Number Theory 11G30, 14G22 |
| url | https://arxiv.org/abs/1912.08043 |