General Serre weight conjectures
Number Theory
2021-03-29 v3
Abstract
We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL(n) over an arbitrary number field, motivated by the formalism of the Breuil-M\'ezard conjecture. We give evidence for these conjectures, and discuss their relationship to previous work. We generalise one of these conjectures to the case of connected reductive groups which are unramified over Q_p, and we also generalise the second author's previous conjecture for GL(n)/Q to this setting, and show that the two conjectures are generically in agreement.
Cite
@article{arxiv.1509.02527,
title = {General Serre weight conjectures},
author = {Toby Gee and Florian Herzig and David Savitt},
journal= {arXiv preprint arXiv:1509.02527},
year = {2021}
}
Comments
Essentially final version, to appear in J. Eur. Math. Soc. This version will not incorporate any minor changes made in proof