## Abstract

Let F be a totally real field, p ≧ 3 a rational prime unramified in F, and p a place of F over p. Let p : Gal(F̄ / F) → GL _{2}(double-struck F sign̄_{p} 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 p to inertia at p, which contains all the modular weights for p. This proves part of a conjecture of Diamond, Buzzard, and Jarvis, which provides an analogue of Serre's epsilon conjecture for Hilbert modular forms mod p.

Original language | English |
---|---|

Pages (from-to) | 57-94 |

Number of pages | 38 |

Journal | Journal fur die Reine und Angewandte Mathematik |

Issue number | 622 |

DOIs | |

State | Published - Sep 2008 |

Externally published | Yes |

### Bibliographical note

Funding Information:The author was supported by the NDSEG and NSF Graduate Research Fellowships.

### Funding

The author was supported by the NDSEG and NSF Graduate Research Fellowships.

Funders | Funder number |
---|---|

National Science Foundation | |

National Defense Science and Engineering Graduate |