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Potential level-lowering for GSp(4)

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  30 January 2009

Claus M. Sorensen
Claus M. Sorensen
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA, ([email protected]).
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Abstract

In this article, we explore a beautiful idea of Skinner and Wiles in the context of GSp(4) over a totally real field. The main result provides congruences between automorphic forms which are Iwahori-spherical at a certain place ω, and forms with a tamely ramified principal series at ω, Thus, after base change to a finite solvable totally real extension, one can often lower the level at ω. For the proof, we first establish an analogue of the Jacquet–Langlands correspondence, using the stable trace formula. The congruences are then obtained on inner forms, which are compact at infinity modulo the centre, and split at all the finite places. The crucial ingredient allowing us to do so, is an important result of Roche on types for principal series representations of split reductive groups.

Keywords

Hilbert–Siegel modular formslevel-lowering congruencestrace formula

MSC classification

Secondary: 11F33: Congruences for modular and $p$-adic modular forms 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F80: Galois representations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 3 , July 2009 , pp. 595 - 622
Copyright
Copyright © Cambridge University Press 2009

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