The $(p,t,a)$-inertial groups as finite monodromy groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909784254447616 |
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| author | Philip, Séverin |
| author_facet | Philip, Séverin |
| contents | Silverberg and Zarhin introduced the notion of a $(p,t,a)$-inertial group in the hope of having a group theoretic characterization of the finite groups that appear as finite monodromy groups -- the groups that represent the local obstruction to semi-stable reduction -- of abelian varieties in fixed dimension $t+a$. In this text, we provide a positive answer to their question, that is, every $(p,t,a)$-inertial group is the finite monodromy group of an abelian variety in dimension $t+a$. To prove this, we show a structure theorem on the rational group algebra $\mathbf{Q}[G]$ of ramification groups, refining a theorem of Serre and generalizing results on $p$-groups of Roquette and Ford. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $(p,t,a)$-inertial groups as finite monodromy groups Philip, Séverin Number Theory Algebraic Geometry Silverberg and Zarhin introduced the notion of a $(p,t,a)$-inertial group in the hope of having a group theoretic characterization of the finite groups that appear as finite monodromy groups -- the groups that represent the local obstruction to semi-stable reduction -- of abelian varieties in fixed dimension $t+a$. In this text, we provide a positive answer to their question, that is, every $(p,t,a)$-inertial group is the finite monodromy group of an abelian variety in dimension $t+a$. To prove this, we show a structure theorem on the rational group algebra $\mathbf{Q}[G]$ of ramification groups, refining a theorem of Serre and generalizing results on $p$-groups of Roquette and Ford. |
| title | The $(p,t,a)$-inertial groups as finite monodromy groups |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2503.21199 |