Positive characteristic Manin-Mumford theorem

TL;DR

This paper proves a version of the Manin-Mumford conjecture for semiabelian varieties over fields of positive characteristic, utilizing model theory of difference fields, extending previous algebraic proofs.

Contribution

It provides a new proof of the Manin-Mumford conjecture in positive characteristic using model theory, complementing existing algebraic approaches.

Findings

Established the conjecture for semiabelian varieties in positive characteristic.

Used model theory of difference fields for the proof.

Connected model-theoretic methods with diophantine geometry.

Abstract

We prove a version of the Manin-Mumford conjecture for semiabelian varieties over fields of positive characteristic. The proof presented here contains the details of the proof sketched by the author in the article "Diophantine geometry from model theory," BSL 7 (2001) no. 1, 37 - 57; using the model theory of difference fields along the lines of Hrushovski. Algebraic proofs have been presented by Pink & Roessler and Pillay.