On the characterization of abelian varieties in characteristic $p>0$

TL;DR

This paper studies the properties and classification of abelian varieties over fields with characteristic p>0, providing insights into their structure and behavior in positive characteristic settings.

Contribution

It offers new arguments and perspectives on abelian varieties in characteristic p>0, distinct from those in the subsequent work 1703.06631.

Findings

Different argument techniques for special cases

Enhanced understanding of abelian varieties in characteristic p

Foundational results for further research

Abstract

This article is superseded by 1703.06631. We keep this version here since some of the arguments for the special cases treated here are different than those of 1703.06631.