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Galois representations associated to holomorphic limits of discrete series

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  26 November 2013

Wushi Goldring  and
Sug Woo Shin
Wushi Goldring
Affiliation:
Département de Mathématiques, Institut Galilée, Université Paris 13, 99 avenue J.B. Clément, 93430 Villetaneuse, France email [email protected]
Sug Woo Shin
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA 02139, USA email [email protected] Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea
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Abstract

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Generalizing previous results of Deligne–Serre and Taylor, Galois representations are attached to cuspidal automorphic representations of unitary groups whose Archimedean component is a holomorphic limit of discrete series. The main ingredient is a construction of congruences, using the Hasse invariant, that is independent of $q$-expansions.

MSC classification

Secondary: 11F33: Congruences for modular and $p$-adic modular forms 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F55: Other groups and their modular and automorphic forms (several variables)
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 2 , February 2014 , pp. 191 - 228
Copyright
© The Author(s) 2013 

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