A hyperbolic Ax-Lindemann theorem in the cocompact case

A hyperbolic Ax-Lindemann theorem in the cocompact case

Thu, 10/11/2011
16:00 		Andrei Yafaev (UCL) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
A hyperbolic Ax-Lindemann theorem in the cocompact case
This is a joint work with Emmanuel Ullmo. This work is motivated by J.Pila's strategy to prove the Andre-Oort conjecture. One ingredient in the strategy is the following conjecture: Let S be a Shimura variety uniformised by a symmetric space X. Let V be an algebraic subvariety of S. Maximal algebraic subvarieties of the preimage of V in X are precisely the components of the preimages of weakly special subvarieties contained in V. We will explain the proof of this conjecture in the case where S is compact.