The isotrivial case in the Mordell-Lang conjecture for semiabelian varieties defined over fields of positive characteristic

TL;DR

This paper investigates the intersection properties of subvarieties with finitely generated subgroups within semiabelian varieties over fields of positive characteristic, extending understanding of the Mordell-Lang conjecture in this setting.

Contribution

It provides a description of the intersection of subvarieties with finitely generated subgroups for semiabelian varieties over fields of positive characteristic, addressing a case of the Mordell-Lang conjecture.

Findings

Characterization of intersections in positive characteristic

Extension of Mordell-Lang conjecture results

New techniques for semiabelian varieties

Abstract

Let G be a semiabelian variety defined over a finite subfield of an algebraically closed field K of prime characteristic. We describe the intersection of a subvariety X of G with a finitely generated subgroup of G(K).