Around the Mordell-Lang and Manin-Mumford conjectures in positive characteristic

TL;DR

This paper proves that the Manin-Mumford conjecture implies the Mordell-Lang conjecture in positive characteristic using integral models and jet schemes, completing a key step in understanding rational points on algebraic varieties.

Contribution

It provides a complete proof of the implication from Manin-Mumford to Mordell-Lang in positive characteristic, employing novel techniques involving integral models and jet schemes.

Findings

Established the implication in positive characteristic.

Utilized integral models of semi-abelian varieties.

Applied jet schemes to algebraic geometry problems.

Abstract

We give a complete proof for the implication from the Manin-Mumford conjecture to the Mordell-Lang conjecture in positive characteristic, using integral models of semi-abelian varieties over a ring of formal power series, and the machinery of jet schemes.