Proof of the Mardell-Lang Conjecture for function fields: 20 years later (Model theoretic aspects of the notion of independence and dimension)

Abstract

Hrushovski's celebrated Theorem 1.1 in [H96] proved the function field Mordell-Lang conjecture. In his proof highly sophisticated model theoretic arguments of Zariski geometry played crucial roles. As a continuous effort of removing Zariski geometry arguments, the authors of [BBPa], [BBPb], [BBPc] succeeded recently to prove Hrushovski's theorem by reducing to the function field Manin-Mumford conjecture without the dichotomy theorem of Zariski geometry. I report here outline of their arguments.