Serre weights for mod p Hilbert modular forms: The totally ramified case

摘要

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 exceptions.