A trace formula approach to control theorems for overconvergent automorphic forms

Abstract

We present an approach to proving control theorems for overconvergent automorphic forms on Harris–Taylor unitary Shimura varieties based on a comparison between the rigid cohomology of the multiplicative ordinary locus and the rigid cohomology of the overlying Igusa tower, the latter which may be computed using the Harris–Taylor version of the Langlands–Kottwitz method. We also prove a higher level version, generalizing work of Coleman.