Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C

2012/08/05 by Christian Johansson, Johansson, Christian
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1208.1034

31 pages. Essentially final version. Hypothesis on p removed from previous version. Accepted, to appear in Math. Annalen

arxiv created 2013/01/21 · arxiv updated 2013/01/22

Abstract

We study the rigid cohomology of the ordinary locus in some compact PEL Shimura varieties of type C with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent Hecke eigenforms. This generalises the work of Coleman, and is a first step in an ongoing project to extend the cohomological approach to classicality to higher-dimensional Shimura varieties.

Related

• Families of coherent PEL automorphic forms
• Eigenvarieties for cuspforms over PEL type Shimura varieties with dense ordinary locus
• p-adic families of automorphic forms over some unitary Shimura varieties
• Systems of Hecke eigenvalues on subschemes of Shimura varieties
• A trace formula approach to control theorems for overconvergent automorphic forms