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arXiv · 1610.04819

Weight elimination in Serre-type conjectures

Daniel Le·Bao V. Le Hung·Brandon Levin
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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. 2016-10-16. Weight elimination in Serre-type conjectures. https://doi.org/10.1215/00127094-2019-0015

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