NT&AG: Ehud de Shalit (HUJI), "Geometry modulo p of some unitary Shimura varieties"

Abstract: This talk will be about joint work with Eyal Goren about the
structure of Picard modular surfaces at a prime p which is inert in the
underlying quadratic imaginary field. The main tool for studying the bad
reduction of Shimura varieties is the theory of local models (due to de
Jong and Rapoport-Zink). Our results concern global geometric questions
which go beyond the theory of global models. For example, we are able to
count supersingular curves on the Picard surface. We also study certain
foliations in its tangent bundle that have not been studied before, and
lead to new conjectures of "Andre-Oort" type. Some of the results should
generalize to other unitary Shimura varieties, but the talk will focus on
U(2,1).

Date: 

Mon, 02/01/2017 - 14:00 to 15:00

Location: 

Ros Building, 70A