The buzzard-diamond-jarvis conjecture for unitary groups

By T. Gee, Tongyin Liu, David Savitt. 2012

72 citations recorded by the source corpus.

Let p > 2 be prime. We prove the weight part of Serre’s conjecture for rank two unitary groups for mod p representations in the unramified case (that is, the Buzzard–Diamond–Jarvis conjecture for unitary groups), by proving that any Serre weight which occurs is a predicted weight. Our methods are purely local, using the theory of (φ, Ĝ)-modules to determine the possible reductions of certain two-dimensional crystalline representations.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/51e9181657c27e708396d7cc6a4cb1762d880a90

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In Geometry and Topology

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

In Mathematical Physics

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

Citations in the corpus

• THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS (2012, methodology): “We remark that, in the case of indefinite quaternion algebras, another proof of the BDJ conjecture (which, like the proof given in this paper, relies on the version of the conjecture for unitary groups proven in [BLGG13a], [GLS13a], [GLS13b]) is given in [New13].”
• Lattices in the cohomology of Shimura curves (2013, methodology): “of both Sections 6 and 7 (or at least enough of them to prove the main results of Sections 8–10) without using these results. We LATTICES IN THE COHOMOLOGY OF SHIMURA CURVES 71 will still make use of [GLS12] in order to prove Theorem 7.1.1, but we remark that it should be possible to establish all o”