Unramifiedness of Galois representations attached to weight one Hilbert modular eigenforms mod p

Abstract

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight 1. The proof is based on the observation that parallel weight 1 forms in characteristic p embed into the ordinary part of parallel weight p forms in two different ways per prime dividing p, namely via `partial' Frobenius operators.

24 pages; minor changes compared to previous version; accepted for publication in the Journal of the Institute of Mathematics of Jussieu

References in corpus (1)

• Explicit Methods for Hilbert Modular Forms of Weight 1

Cited by in corpus (5)

• A Serre weight conjecture for geometric Hilbert modular forms in characteristic p
• Compactifications of Iwahori-level Hilbert modular varieties
• Unramifiedness of weight one Hilbert Hecke algebras
• Kodaira-Spencer isomorphisms and degeneracy maps on Iwahori-level Hilbert modular varieties: the saving trace
• Unramifiedness of Galois representations arising from Hilbert modular surfaces