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- Toby Gee
- 2011

We prove a variety of results on the existence of automorphic Galois representations lifting a residual automorphic Galois representation. We prove a result on the structure of deformation rings of… (More)

- Toby Gee
- 2006

We prove a modularity lifting theorem for potentially Barostti-Tate representations over totally real fields, generalising recent results of Kisin.

- Toby Gee
- 2011

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… (More)

We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call ‘potential diagonalizability’. This result allows for ‘change of weight’ and… (More)

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… (More)

- Toby Gee, Mark Kisin
- 2014

We prove the Breuil–Mézard conjecture for 2-dimensional potentially Barsotti–Tate representations of the absolute Galois group GK , K a finite extension of Qp, for any p > 2 (up to the question of… (More)

Under mild hypotheses, we prove that if F is a totally real field, and ρ : GF → GL2(Fl) is irreducible and modular, then there is a finite solvable totally real extension F /F such that ρ|GF ′ has a… (More)

We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations… (More)

We use the patching method of Taylor–Wiles and Kisin to construct a candidate for the p-adic local Langlands correspondence for GLn(F ), F a finite extension of Qp. We use our construction to prove… (More)

- Toby Gee, Kevin Buzzard, +9 authors Sug Woo Shin
- 2013