Point-Counting and the Zilber-Pink Conjecture (4/4)

par Jonathan Pila (University of Oxford & IHES)

mardi 12 mars 2024, 10:30 → 12:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

The Zilber-Pink conjecture is a diophantine finiteness conjecture. It unifies and gives a far-reaching generalization of the classical Mordell-Lang and Andre-Oort conjectures, and is wide open in general.
Point-counting results for definable sets in o-minimal structures provide a strategy for proving suitable cases which has had some success, in particular in its use in proving the Andre-Oort conjecture.
The course will describe the Zilber-Pink conjecture and the point-counting approach to proving cases of it, eventually concentrating on the case of a curve in a power of the modular curve.
We will describe the model-theoretic contexts of the conjectures and techniques, and the essential arithmetic ingredients.

Vidéo