| Résume | The classical theory of abstract projective geometries establishes an equivalence between axiomatically defined incidence systems of points and lines and projective planes defined over a field. Zilber's Restricted Trichotomy conjecture in dimension one is a generalization of this statement in a sense, with lines replaced by algebraic curves; it implies that a non-locally modular strongly minimal structure with the universe an algebraic curve over an algebraically closed field and basic relations constructible subsets of Cartesian powers of the curve interprets an infinite field. The talk will present the basic structure of the proof of the conjecture, and outline its application, by Zilber, to Torreli-type theorem for curves over finite fields of Bogomolov, Korotiaev and Tschinkel. Joint work with Assaf Hasson. |
