Overconvergent algebraic automorphic forms

Details Overconvergent algebraic automorphic forms Overconvergent algebraic automorphic forms

2009-01-15

arxiv.org/abs/0901.2279v2

Proc. London Math. Soc. 102 (2011), No. 2, p. 193--228

Mathematics

Number Theory

36 pages, completely revised version including several additional results (e.g. comparison with Emerton's theory). To appear i

Scientific paper

10.1112/plms/pdq019

I present a general theory of overconvergent p-adic automorphic forms and eigenvarieties 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 GL(n). 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.

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