Groupes de monodromie finie des variétés abéliennes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915066113163264 |
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| author | Philip, Séverin |
| author_facet | Philip, Séverin |
| contents | The finite monodromy groups of abelian varieties over number fields have been introduced by Grothendieck. They represent the local obstruction to semi-stable reduction. In this paper we prove a criteria for finite groups to be realized as finite monodromy groups in given dimension. An application to the degree of semi-stability gives an effective version of Grothendieck's semi-stable reduction theorem in terms of the degree of the extension with regards to the dimension of the variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Groupes de monodromie finie des variétés abéliennes Philip, Séverin Number Theory Algebraic Geometry The finite monodromy groups of abelian varieties over number fields have been introduced by Grothendieck. They represent the local obstruction to semi-stable reduction. In this paper we prove a criteria for finite groups to be realized as finite monodromy groups in given dimension. An application to the degree of semi-stability gives an effective version of Grothendieck's semi-stable reduction theorem in terms of the degree of the extension with regards to the dimension of the variety. |
| title | Groupes de monodromie finie des variétés abéliennes |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2412.11900 |