Classicality of overconvergent automorphic forms on some Shimura varieties
Author(s)
Johansson, Hans Christian
Type
Thesis
Abstract
This thesis consists of two parts. In Part 1 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, generalizing work of Coleman.
In part 2 we compare the conjecture of Buzzard-Gee on the association of
Galois representations to C-algebraic automorphic representations with the conjectural
description of the cohomology of Shimura varieties due to Kottwitz, and
the reciprocity law at infinity due to Arthur. This is done by extending Langlands's
representation of the L-group associated with a Shimura datum to a representation
of the C-group of Buzzard-Gee. The approach offers an explanation of the explicit
Tate twist appearing in Kottwitz's description.
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, generalizing work of Coleman.
In part 2 we compare the conjecture of Buzzard-Gee on the association of
Galois representations to C-algebraic automorphic representations with the conjectural
description of the cohomology of Shimura varieties due to Kottwitz, and
the reciprocity law at infinity due to Arthur. This is done by extending Langlands's
representation of the L-group associated with a Shimura datum to a representation
of the C-group of Buzzard-Gee. The approach offers an explanation of the explicit
Tate twist appearing in Kottwitz's description.
Version
Open Access
Date Issued
2013-03
Date Awarded
2013-07
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Buzzard, Kevin
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)