On Hermitian forms over dyadic non-maximal local orders

TL;DR

This paper classifies skew-Hermitian modules over dyadic non-maximal local orders, simplifying the study of polarized abelian varieties over finite fields by reducing it to an algebraic classification problem.

Contribution

It provides a complete classification of skew-Hermitian modules over dyadic non-maximal local orders, advancing understanding in algebraic and arithmetic geometry.

Findings

Complete classification of skew-Hermitian modules over dyadic non-maximal local orders

Reduction of polarized abelian varieties over finite fields to algebraic modules

New algebraic tools for studying non-maximal local orders

Abstract

We reduce a study of polarized abelian varieties over finite fields to the classification problem of skew-Hermitian modules over (possibly non-maximal) local orders. The main result of this paper gives a complete classification of these skew-Hermitian modules in the case when the ground ring is a dyadic non-maximal local order.