Weights in Serre's conjecture for Hilbert modular forms: the ramified case

Details Weights in Serre's conjecture for Hilbert modular forms: the ramified case Weights in Serre's conjecture for Hilbert modular forms: the ramified case

2006-10-16

arxiv.org/abs/math/0610488v2

Mathematics

Number Theory

Notation improved and typos corrected; to appear in Israel J. Math

Scientific paper

Let F be a totally real field and p an odd prime. If r is a continuous, semisimple, totally odd mod p representation of the absolute Galois group of F which is tamely ramified at all places of F dividing p, then we formulate a conjecture specifying the weights for which r is modular. This extends the conjecture of Diamond, Buzzard, and Jarvis, which supposed that p was unramified in F. We also prove a theorem towards the conjecture and provide some computational evidence.

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