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arXiv · 2412.11900

Groupes de monodromie finie des variétés abéliennes

Séverin Philip
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Abstract

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.

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Séverin Philip. 2024-12-16. Groupes de monodromie finie des variétés abéliennes. https://arxiv.org/abs/2412.11900

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