@article{75fdad97d1b14340a422e85c23cddf0d,
title = "Weight elimination in serre-type conjectures",
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.",
author = "Daniel Le and Hung, {Bao V.Le} and Brandon Levin",
note = "Funding Information: Le{\textquoteright}s work was supported by the National Science Foundation under agreement numbers DMS-1128155 and DMS-1703182 and an American Mathematical Society– Simons travel grant. Le Hung{\textquoteright}s work was supported in part by the National Science Foundation under grant number DMS-1802037. Funding Information: We would like to thank Matthew Emerton, Thomas Haines, Florian Herzig, and Stefano Morra for many helpful conversations, and Florian Herzig for detailed comments on an earlier draft of this paper. We thank the referees for very detailed and helpful feedback which greatly improved the paper. We would also like to thank the Institut Henri Poincar? for their hospitality during part of this project. Le's work was supported by the National Science Foundation under agreement numbers DMS-1128155 and DMS-1703182 and an American Mathematical Society- Simons travel grant. Le Hung's work was supported in part by the National Science Foundation under grant number DMS-1802037. Publisher Copyright: {\textcopyright} 2019 Duke University Press. All rights reserved.",
year = "2019",
doi = "10.1215/00127094-2019-0015",
language = "English (US)",
volume = "168",
pages = "2433--2506",
journal = "Duke Mathematical Journal",
issn = "0012-7094",
publisher = "Duke University Press",
number = "13",
}