The local obstruction to semi-stable reduction for abelian varieties

2025/11/07 by Philip, Séverin
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.2511.05127

openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

Abstract

Grothendieck defined a group that represents the local obstruction for an abelian variety to have semi-stable reduction. These groups were studied by Silverberg and Zarhin and more recently by the author in order to give a group theoretic characterization of them depending only on the dimension. We give an overview of the developments since Grothendieck's definition with the added novelty of the case of equal characteristic local fields.

Citations

• Variétés abéliennes CM et grosse monodromie finie sauvage
• Subgroups of inertia groups arising from abelian varieties
• Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques
• Good Reduction of Abelian Varieties

Related

• Groupes de monodromie finie des variétés abéliennes
• Reduction of Abelian Varieties and Grothendieck's Pairing
• Subgroups of inertia groups arising from abelian varieties
• On the degree of semi-stable reduction
• Reduction of abelian varieties