Groupes de monodromie finie des vari\'et\'es ab\'eliennes

TL;DR

This paper establishes criteria for finite groups to be realized as monodromy groups of abelian varieties over number fields, providing an effective version of Grothendieck's semi-stable reduction theorem based on the degree of extension.

Contribution

It introduces new criteria for finite monodromy groups of abelian varieties and offers an effective semi-stable reduction theorem in relation to the variety's dimension.

Findings

Criteria for finite monodromy groups established

Effective bounds for semi-stable reduction provided

Application to the degree of extension in reduction process

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.