General Serre weight conjectures

Toby Gee, Florian Herzig, David Savitt

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GLn over an arbitrary number field, motivated by the formalism of the Breuil-Mézard 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 Qp, and we also generalise the second author's previous conjecture for GLn/Q to this setting, and show that the two conjectures are generically in agreement.

Original languageEnglish (US)
Pages (from-to)2859-2949
Number of pages91
JournalJournal of the European Mathematical Society
Volume20
Issue number12
DOIs
StatePublished - Jan 1 2018

Keywords

  • Automorphic representations
  • Breuil-Mézard conjecture
  • Crystalline representations
  • Galois representations
  • L-parameters
  • Mod p Langlands correspondence
  • Patching functors
  • Serre weight
  • Serre's conjecture

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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