Loeffler, David. (2011) Overconvergent algebraic automorphic forms. Proceedings of the London Mathematical Society, Vol.102 (No.2). pp. 193-228. ISSN 0024-6115

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Abstract

A general theory of overconvergent p-adic modular forms and eigenvarieties is presented for connected reductive algebraic groups G whose real points are compact modulo centre, extending earlier constructions due to Buzzard, Chenevier and Yamagami for forms of GLn. This leads to some new phenomena, including the appearance of intermediate spaces of ‘semi-classical’ automorphic forms; this gives a hierarchy of interpolation spaces (eigenvarieties) interpolating classical automorphic forms satisfying different finite slope conditions (corresponding to a choice of parabolic subgroup of G at p). The construction of these spaces relies on methods of locally analytic representation theory, combined with the theory of compact operators on Banach modules.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Automorphic forms, Forms, Modular, Convergence, Linear algebraic groups
Journal or Publication Title:	Proceedings of the London Mathematical Society
Publisher:	Oxford University Press
ISSN:	0024-6115
Date:	February 2011
Volume:	Vol.102
Number:	No.2
Page Range:	pp. 193-228
Identification Number:	10.1112/plms/pdq019
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EPSRC (EP/F04304X/1)
URI:	http://wrap.warwick.ac.uk/id/eprint/37072

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