Israel Journal of Mathematics

, Volume 166, Issue 1, pp 369–391

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

Article

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

Abstract

Let F be a totally real field and p ≥ 3 a prime. If ρ :
https://static-content.springer.com/image/art%3A10.1007%2Fs11856-008-1035-9/MediaObjects/11856_2008_1035_Fig1_HTML.jpg
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

Authors and Affiliations

  1. 1.Institute of MathematicsHebrew University of JerusalemGivat Ram, JerusalemIsrael