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

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Let F be a totally real field and p ≥ 3 a prime. If ρ : Gal(F̄/F) → GL2 (|double strok F sign̄p) is continuous, semisimple, totally odd, and tamely ramified at all places of F dividing p, then we formulate a conjecture specifying the weights for which ρ is modular. This extends the conjecture of Diamond, Buzzard, and Jarvis, which required p to be unramified in F. We also prove a theorem that verifies one half of the conjecture in many cases and use Dembélé's computations of Hilbert modular forms over ℚ(√5 ) to provide evidence in support of the conjecture.

Original languageEnglish
Pages (from-to)369-391
Number of pages23
JournalIsrael Journal of Mathematics
StatePublished - Aug 2008
Externally publishedYes

Bibliographical note

Funding Information:
∗ The author thanks the NSF for a Graduate Research Fellowship that supported him during part of this work. Received October 16, 2006 and in revised form February 14, 2007


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