1,746 research outputs found
D-modules on rigid analytic spaces
We give an overview of the theory of \wideparen{\mathcal{D}}-modules on
rigid analytic spaces and its applications to admissible locally analytic
representations of -adic Lie groups.Comment: to appear in the Proceedings of the IC
A trace formula approach to control theorems for overconvergent automorphic forms
We present an approach to proving control theorems for overconvergent
automorphic forms on some Harris-Taylor unitary Shimura varieties based on a
comparison between the rigid coho- mology of the multiplicative ordinary locus
and the rigid cohomology of the overlying Igusa tower, the latter which may be
computed using the Harris-Taylor version of the Langlands-Kottwitz method. We
also prove a higher level version, generalizing work of Coleman.Comment: 25 pages. Main results strengthened, higher level version include
Zero-loci of Brauer group elements on semi-simple algebraic groups
We consider the problem of counting the number of rational points of bounded
height in the zero-loci of Brauer group elements on semi-simple algebraic
groups over number fields. We obtain asymptotic formulae for the counting
problem for wonderful compactifications using the spectral theory of
automorphic forms. Applications include asymptotic formulae for the number of
matrices over Q whose determinant is a sum of two squares. These results
provide a positive answer to some cases of a question of Serre concerning such
counting problems.Comment: 35 pages. Added more details and fixed typos. Final versio
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