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

By Michael M. Schein. 2006

51 citations recorded by the source corpus.

AbstractLet 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d93cffb77a86b6f95317d28f7a11de1870b0896a

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In Algebra and Number Theory

1. C. Breuil

In Geometry and Topology

1. C. Breuil
2. Peter Scholze
3. Vytautas Paškūnas
4. M. Kisin
5. T. Gee
6. B. Bhatt
7. Tongyin Liu
8. Laurent Berger

In Mathematical Physics

1. C. Breuil
2. Peter Scholze
3. Vytautas Paškūnas
4. M. Kisin
5. B. Bhatt
6. Tongyin Liu
7. T. Gee
8. Laurent Berger

Citations in the corpus

• The emerging p-adic Langlands programme (2011, background): “We have seen in §3 that the set of Serre weightsW(ρ) associated in [18] and [58] to a linear continuous 2-dimensional representation of Gal(Qp/F ) over kE is expected to be the set of simple summands (forgetting possible multiplicities) of the GL2(OF )F×-socle of some smooth admissible representatio”