Torsion of abelian varieties and Lubin-Tate extensions

TL;DR

This paper proves that the torsion subgroup of an abelian variety with potential good reduction over a p-adic field, when considered over a composite of the field and a Lubin-Tate extension, is finite.

Contribution

It establishes the finiteness of torsion points of abelian varieties over composite fields involving Lubin-Tate extensions, extending understanding of torsion in p-adic contexts.

Findings

Torsion subgroup is finite over the composite field.

Potential good reduction implies torsion finiteness.

Results apply to abelian varieties over p-adic fields.

Abstract

We show that, for an abelian variety defined over a $p$-adic field $K$ which has potential good reduction, its torsion subgroup with values in the composite field of $K$ and a certain Lubin-Tate extension over a $p$-adic field is finite.