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

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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · semigroups and automata theory
