General Serre weight conjectures

  • Toby Gee

    Imperial College London, UK
  • Florian Herzig

    University of Toronto, Canada
  • David Savitt

    The Johns Hopkins University, Baltimore, USA


We formulate a number of related generalisations of the weight part of Serre’s conjecture to the case of GL 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 , and we also generalise the second author’s previous conjecture for GL to this setting, and show that the two conjectures are generically in agreement.

Cite this article

Toby Gee, Florian Herzig, David Savitt, General Serre weight conjectures. J. Eur. Math. Soc. 20 (2018), no. 12, pp. 2859–2949

DOI 10.4171/JEMS/826