Weights in Serre’s Conjecture for Hilbert Modular Forms: the Ramified Case
نویسنده
چکیده
Abstract. Let F be a totally real field and p ≥ 3 a prime. If ρ : Gal(F/F ) → GL2(Fp) is continuous, semisimple, totally odd, and tamely ramified at all places of F dividing p, then we formulate a conjecture specifying the weights for which ρ is modular. This extends the conjecture of Diamond, Buzzard, and Jarvis, which required p to be unramified in F . We also prove a theorem that verifies one half of the conjecture in many cases and use Dembélé’s computations of Hilbert modular forms over Q( √ 5) to provide evidence in support of the conjecture.
منابع مشابه
Weights 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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