37 citations · 333 across the 52 of their papers we have counts for
4 papers · 1 filter
Patching and the p-adic local Langlands correspondence
Ana Caraiani, Matthew Emerton, Toby Gee +3
We use the patching method of Taylor--Wiles and Kisin to construct a candidate for the p-adic local Langlands correspondence for GL_n(F), F a finite extension of Q_p. We use our co…
The weight part of Serre's conjecture for GL(2)
Toby Gee, Tong Liu, David Savitt
Let p > 2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call "pseudo-Barsotti-Tate rep…
The Breuil--Mezard conjecture for quaternion algebras
Toby Gee, David Geraghty
We formulate a version of the Breuil--Mezard conjecture for quaternion algebras, and show that it follows from the Breuil--Mezard conjecture for GL_2. In the course of the proof we…
Lattices in the cohomology of Shimura curves
Matthew Emerton, Toby Gee, David Savitt
We prove conjectures of Breuil and Breuil-Dembele (C. Breuil, "Sur un probleme de compatibilite local-global modulo p pour GL(2)"), including a generalisation from the principal se…