Berger, T. orcid.org/0000-0002-5207-6221 and Weiss, A. (2022) Lafforgue pseudocharacters and parities of limits of Galois representations. manuscripta mathematica, 168 (1-2). pp. 225-256. ISSN 0025-2611
Abstract
Let F be a CM field with totally real subfield F+ and let π be a C-algebraic cuspidal automorphic representation of the unitary group U(a,b)(AF+), whose archimedean components are discrete series or non-degenerate limit of discrete series representations. We attach to π a Galois representation Rπ:Gal(F¯¯¯¯/F+)→CU(a,b)(Q¯¯¯¯ℓ) such that, for any complex conjugation element c, Rπ(c) is as predicted by the Buzzard–Gee conjecture (Buzzard and Gee, in: Automorphic forms and Galois representa, Cambridge University Press, Cambridge, 2014). As a corollary, we deduce that the Galois representations attached to certain irregular, C-algebraic essentially conjugate self-dual cuspidal automorphic representations of GLn(AF) are odd in the sense of Bellaïche–Chenevier (Compos Math 147(5):1337–1352, 2011).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. This is an author-produced version of a paper subsequently published in manuscripta mathematica. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | math.NT; math.NT |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 26 Apr 2021 11:38 |
Last Modified: | 26 May 2022 13:31 |
Status: | Published |
Publisher: | Springer Nature |
Refereed: | Yes |
Identification Number: | 10.1007/s00229-021-01305-7 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:173198 |