On the weights of mod p Hilbert modular forms
نویسندگان
چکیده
منابع مشابه
ON THE WEIGHTS OF MOD p HILBERT MODULAR FORMS
We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod p Hilbert modular forms, by making use of modularity lifting theorems and computations in p-adic Hodge theory.
متن کاملSERRE WEIGHTS FOR MOD p HILBERT MODULAR FORMS: THE TOTALLY RAMIFIED CASE
We study the possible weights of an irreducible 2-dimensional modular mod p representation of Gal(F/F ), where F is a totally real field which is totally ramified at p, and the representation is tamely ramified at the prime above p. In most cases we determine the precise list of possible weights; in the remaining cases we determine the possible weights up to a short and explicit list of excepti...
متن کاملSERRE WEIGHTS FOR MOD p HILBERT MODULAR FORMS: THE TOTALLY RAMIFIED CASE TOBY GEE AND DAVID SAVITT
We study the possible weights of an irreducible 2-dimensional modular mod p representation of Gal(F/F ), where F is a totally real field which is totally ramified at p, and the representation is tamely ramified at the prime above p. In most cases we determine the precise list of possible weights; in the remaining cases we determine the possible weights up to a short and explicit list of excepti...
متن کاملSIEGEL MODULAR FORMS ( MOD p ) AND ALGEBRAIC MODULAR FORMS
In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...
متن کاملWeights of Galois Representations Associated to Hilbert Modular Forms
Let F be a totally real field, p ≥ 3 a rational prime unramified in F , and p a place of F over p. Let ρ : Gal(F/F ) → GL2(Fp) 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 ρ to inertia at p, which contains all the ...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2010
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-010-0284-5