On the weights of mod p Hilbert modular forms

By T. Gee. 2006

61 citations recorded by the source corpus.

We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod p Hilbert modular forms, by making use of modularity lifting theorems and computations in p-adic Hodge theory.

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

View Paper: https://www.semanticscholar.org/paper/66ceb792ad4e7f90b1e5243ac06fd2010d6e0533

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In Algebra and Number Theory

1. M. Kisin
2. David Savitt
3. M. Emerton
4. Tongyin Liu
5. T. Gee
6. Frank Calegari
7. David Loeffler
8. K. Lai

In Geometry and Topology

1. T. Gee
2. M. Emerton
3. David Savitt
4. M. Kisin
5. Tongyin Liu
6. David Geraghty
7. J. Thorne
8. Vytautas Paškūnas

In Mathematical Physics

1. T. Gee
2. M. Emerton
3. David Savitt
4. M. Kisin
5. Tongyin Liu
6. David Geraghty
7. J. Thorne
8. Vytautas Paškūnas

Citations in the corpus

• A Modularity Lifting Theorem for Weight Two Hilbert Modular Forms (2006, methodology): “residue field at v is not F p”, and to note that Theorem 3.4.11 of [Kis04] is still valid in the context in which we need it, by Proposition 2.3. For the applications to mod p Hilbert modular forms in [Gee06] it is important not to have to assume that ρ is potentially ordinary at v if and only if ρ f”
• The buzzard-diamond-jarvis conjecture for unitary groups (2012, methodology): “ecomposable, the description is in terms of certain crystalline extension classes.) Remarks on related papers. Theorem A had previously been established in the case of generic (or regular) weights in [Gee11], by a rather different method. In particular, the regularity hypothesis allowed the author to”
• Automorphic lifts of prescribed types (2008, methodology): “To our knowledge, the only such theorems in the literature are those for weight two Hilbert modular forms in [Kis07c] and [Gee06a], and the work of [Kis06] for modular forms over totally real fields in which p splits completely.”
• THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS (2012, methodology): “In fact, examining the proof of Proposition 3.1.5 of [Gee11a], we see that it is enough to check that there is some finite solvable extension L/F of totally real fields with the property that L is linearly disjoint from F ker ρ (ζp) over F , and ρ|GL has a modular lift which is potentially…”
• Lattices in the cohomology of Shimura curves (2013, methodology): “This proof is related to the approach taken in [Gee11], but avoids both the combinatorial arguments of that paper and the dependence on the modularity lifting theorems proved in [Kis09b, Gee06].”