A model-theoretic approach to problems of Manin-Mumford-Andre-Oort-type.

Mardi 19 janvier 2010 16:00-17:00 - Pila Jonathan - UIniversity of Bristol

Résumé : I will describe a result, joint with Alex Wilkie, about the distribution of rational points on certain non-algebraic sets in real space.
The natural setting is an `o-minimal structure over the real numbers’, a notion from model-theory. A surprising strategy, proposed by Umberto Zannier, uses this result to approach diophantine problems in the Manin-Mumford-Andre-Oort circle of conjectures. I will describe some implementations of this strategy, including an unconditional proof of the Andre-Oort conjecture for products of modular curves.

Lieu : bât. 425 - 113-115

A model-theoretic approach to problems of Manin-Mumford-Andre-Oort-type.  Version PDF