A trace formula approach to control theorems for overconvergent automorphic forms

2013/09/27 by Christian Johansson, Johansson, Christian
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1309.7239

25 pages. Main results strengthened, higher level version included

arxiv created 2015/10/08 · arxiv updated 2015/10/09

Abstract

We present an approach to proving control theorems for overconvergent automorphic forms on some Harris-Taylor unitary Shimura varieties based on a comparison between the rigid coho- mology 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.

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