Subgroups of inertia groups arising from abelian varieties

1997/06/03 by Alice Silverberg, Silverberg, A., Yu. G. Zarhin +1 · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.alg-geom/9706002

openalex publication_date 1997/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an abelian variety over a field with a discrete valuation, Grothendieck defined a certain open normal subgroup of the absolute inertia group. This subgroup encodes information on the extensions over which the abelian variety acquires semistable reduction. We study this subgroup, and use it to obtain information on the extensions over which the abelian variety acquires semistable reduction.

Citations

• Good Reduction of Abelian Varieties

Cited by

• The local obstruction to semi-stable reduction for abelian varieties

Related

• Étale cohomology and reduction of abelian varieties
• The local obstruction to semi-stable reduction for abelian varieties
• Reduction of abelian varieties
• The (p,t,a)-inertial groups as finite monodromy groups
• Reduction of Abelian Varieties and Grothendieck's Pairing