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

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DOI: 10.1007/s11856-008-1035-9

- Cite this article as:
- Schein, M.M. Isr. J. Math. (2008) 166: 369. doi:10.1007/s11856-008-1035-9

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## Abstract

Let

*F*be a totally real field and*p*≥ 3 a prime. If*ρ*: 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 \(\mathbb{Q}(\sqrt 5 )\) to provide evidence in support of the conjecture.## Copyright information

© Hebrew University Magnes Press 2008