The (p,t,a)-inertial groups as finite monodromy groups

2025/03/27 by Séverin Philip, Philip, Séverin
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2503.21199

openalex publication_date 2025/03/27 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

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 Q[G] of ramification groups, refining a theorem of Serre and generalizing results on p-groups of Roquette and Ford.

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• A characterization of ramification groups via Taylor morphism
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