On Hrushovski's proof of the Manin-Mumford conjecture

Abstract

The Manin-Mumford conjecture in characteristic zero was first proved by Raynaud. Later, Hrushovski gave a different proof using model theory. His main result from model theory, when applied to abelian varieties, can be rephrased in terms of algebraic geometry. In this paper we prove that intervening result using classical algebraic geometry alone. Altogether, this yields a new proof of the Manin-Mumford conjecture using only classical algebraic geometry.

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• Geometric Bogomolov conjecture in arbitrary characteristics
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• On $p$-adic versions of the Manin-Mumford Conjecture