Serre Weights for Locally Reducible Two-dimensional Galois Representations
نویسنده
چکیده
Let F be a totally real field, and v a place of F dividing an odd prime p. We study the weight part of Serre’s conjecture for continuous totally odd representations ρ : GF → GL2(Fp) that are reducible locally at v. Let W be the set of predicted Serre weights for the semisimplification of ρ|GFv . We prove that when ρ|GFv is generic, the Serre weights inW for which ρ is modular are exactly the ones that are predicted (assuming that ρ is modular). We also determine precisely which subsets of W arise as predicted weights when ρ|GFv varies with fixed generic semisimplification.
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