Geodesic
General Serre weight conjectures
Journal of the European Mathematical Society, Tome 20 (2018) no. 12, pp. 2859-2949 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/826
Classification : 11-XX
Keywords: Galois representations, automorphic representations, Serre’s conjecture, Serre weight, Breuil–Mézard conjecture, mod p Langlands correspondence, patching functors, crystalline representations, L-parameters 
@article{JEMS_2018_20_12_a0,
     author = {Toby Gee and Florian Herzig and David Savitt},
     title = {General {Serre} weight conjectures},
     journal = {Journal of the European Mathematical Society},
     pages = {2859--2949},
     year = {2018},
     volume = {20},
     number = {12},
     doi = {10.4171/jems/826},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/826/}
}
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Toby Gee; Florian Herzig; David Savitt. General Serre weight conjectures. Journal of the European Mathematical Society, Tome 20 (2018) no. 12, pp. 2859-2949. doi: 10.4171/jems/826

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