Overconvergent algebraic automorphic forms
Loeffler, David. (2011) Overconvergent algebraic automorphic forms. Proceedings of the London Mathematical Society, Vol.102 (No.2). pp. 193-228. ISSN 0024-6115Full text not available from this repository.
Official URL: http://dx.doi.org/10.1112/plms/pdq019
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|
|Official Date:||February 2011|
|Page Range:||pp. 193-228|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC)|
|Grant number:||EPSRC (EP/F04304X/1)|
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