An Algebraic Proof of Hrushovski's Theorem

TL;DR

This paper provides an algebraic geometric proof of Hrushovski's theorem, originally proved using model theory, offering a new perspective in the characteristic p setting.

Contribution

It presents the first purely algebro-geometric proof of Hrushovski's theorem in characteristic p, bypassing model-theoretic methods.

Findings

Algebraic geometric proof of Hrushovski's theorem

Alternative approach in characteristic p

Enhanced understanding of the theorem's foundations

Abstract

In his paper on the Mordell-Lang conjecture, Hrushovski employed techniques from model theory to prove the function field version of the conjecture. In doing so he was able to answer a related question of Voloch, which we refer to henceforth as Hrushovski's theorem. In this paper we shall give an alternative proof of said theorem in the characteristic $p$ setting, but using purely algebro-geometric ideas.