manuscripta mathematica

, Volume 151, Issue 1, pp 19–48

A trace formula approach to control theorems for overconvergent automorphic forms

Article

DOI: 10.1007/s00229-016-0826-2

Cite this article as:
Johansson, C. manuscripta math. (2016) 151: 19. doi:10.1007/s00229-016-0826-2
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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.

Mathematics Subject Classification

11F33 11G18 14F30v 

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA