Weights of Galois representations associated to Hilbert modular forms

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Let F be a totally real field, p ≧ 3 a rational prime unramified in F, and p a place of F over p. Let p : Gal(F̄ / F) → GL 2(double-struck F sign̄p be a two-dimensional mod p Galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible. We specify a set of weights, determined by the restriction of p to inertia at p, which contains all the modular weights for p. This proves part of a conjecture of Diamond, Buzzard, and Jarvis, which provides an analogue of Serre's epsilon conjecture for Hilbert modular forms mod p.

Original languageEnglish
Pages (from-to)57-94
Number of pages38
JournalJournal fur die Reine und Angewandte Mathematik
Issue number622
StatePublished - Sep 2008
Externally publishedYes

Bibliographical note

Funding Information:
The author was supported by the NDSEG and NSF Graduate Research Fellowships.


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