MINIMAL MODELS OF CURVES OF GENUS 2 AND HOMOMORPHISMS OF ABELIAN VARIETIES DEFINED OVER A FIELD OF FINITE CHARACTERISTIC

Abstract

In this article, we prove a finiteness theorem for isogenous abelian varieties of dimension 2 defined over a field of algebraic functions of one variable whose characteristic 2. By means of this result, we prove Tate's conjecture on homomorphisms of abelian varieties of dimension 1 defined over the same field.