10/11/2007

S.W.Shin
Institute for Advanced Study

Counting points on Igusa varieties and stabilization

In the beginning we review the classical method of computing the cohomology of PEL-type Shimura varieties with good reduction modulo p, and explain the tools that are useful for studying the bad reduction of compact Shimura varieties. Then we introduce the counting point formula for Igusa varieties, which plays the role of the analogous formula for the mod p fiber of Shimura varieties with good reduction. Time permitting, we will discuss how our formula can be stabilized.