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15 September 2019 Weight elimination in Serre-type conjectures
Daniel Le, Bao V. Le Hung, Brandon Levin
Duke Math. J. 168(13): 2433-2506 (15 September 2019). DOI: 10.1215/00127094-2019-0015

Abstract

We prove the weight elimination direction of the Serre weight conjectures as formulated by Herzig for forms of U(n) which are compact at infinity and split at places dividing p in generic situations. That is, we show that all modular weights for a mod p Galois representation are contained in the set predicted by Herzig. Under some additional hypotheses, we also show modularity of all the “obvious” weights.

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Daniel Le. Bao V. Le Hung. Brandon Levin. "Weight elimination in Serre-type conjectures." Duke Math. J. 168 (13) 2433 - 2506, 15 September 2019. https://doi.org/10.1215/00127094-2019-0015

Information

Received: 17 February 2017; Revised: 17 January 2019; Published: 15 September 2019
First available in Project Euclid: 10 September 2019

zbMATH: 07131292
MathSciNet: MR4007598
Digital Object Identifier: 10.1215/00127094-2019-0015

Subjects:
Primary: 11F80
Secondary: 11F33, 11F75, 20C33

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 13 • 15 September 2019
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