Class Field Theory and Arithmetic of Abelian Varieties over Local Fields

TL;DR

This paper extends the applicability of a key result about abelian varieties from local fields with finite residue fields to those with arbitrary perfect residue fields of positive characteristic, using local field theory insights.

Contribution

It adapts Lubin and Rosen's proof to broader local fields, expanding the scope of Mazur's Proposition 4.39 to include perfect residue fields.

Findings

Broadened the class of local fields where Mazur's proposition applies

Connected local class field theory with abelian varieties over more general local fields

Provided a framework for future research in arithmetic geometry over diverse local fields

Abstract

We use knowledge of local fields to adapt Jonathan Lubin and Michael Rosen's proof of Mazur's Proposition 4.39. This changes the result about abelian varieties from only working over local fields with a finite residue field to working with local fields with an arbitrary perfect residue field of positive characteristic. We then briefly discuss the Local Class Field Theory implications of such information