English

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

Number Theory 2007-12-30 v2

Abstract

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.

Keywords

Cite

@article{arxiv.math/0610488,
  title  = {Weights in Serre's conjecture for Hilbert modular forms: the ramified case},
  author = {Michael M. Schein},
  journal= {arXiv preprint arXiv:math/0610488},
  year   = {2007}
}

Comments

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