Purely additive reduction of abelian varieties with torsion

2021/11/30 by Melistas, Mentzelos
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2111.15315

Abstract

Let O_K be a discrete valuation ring with fraction field K of characteristic 0 and algebraically closed residue field k of characteristic p > 0. Let A/K be an abelian variety of dimension g with a K-rational point of order p. In this article, we are interested in the reduction properties that A/K can have. After discussing the general case, we specialize to g=1, and we study the possible Kodaira types that can occur.

Related

• A generalization of a theorem of Imai and its applications to Iwasawa theory
• Reduction of abelian varieties
• Semistable reduction of abelian varieties over extensions of small degree
• Abelian Varieties with p-rank Zero
• Torsion of abelian varieties and Lubin-Tate extensions