Date & Time: Friday, October 24, 2008, 16:00-17:00.
Venue: Ramanujan Hall
Title: On Shimura Curves in the Schottky Locus
Speaker: Stefan Kukulies, University of Duisberg-Essen
Abstract: We show that a given rational Shimura curve Y with strictly maximal Higgs field in the moduli space of g-dimensional abelian varieties does not lie in the closure of the Schottky locus for large g. We achieve this by using a result of Viehweg and Zuo which says that if Y lies in the Schottky locus, then the corresponding family of abelian varieties is isogenous over Y to the g-fold product of a modular family of elliptic curves. After reducing the situation from the field of complex numbers to a finite field, we will see, combining the Weil and Sato-Tate conjectures, that this is impossible for large genus g.