37 citations · 333 across the 52 of their papers we have counts for
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Potential automorphy and change of weight
Thomas Barnet-Lamb, Toby Gee, David Geraghty +1
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 `chan…
The conjectural connections between automorphic representations and Galois representations
Kevin Buzzard, Toby Gee
We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them.
Congruences between Hilbert modular forms: constructing ordinary lifts
Thomas Barnet-Lamb, Toby Gee, David Geraghty
Under mild hypotheses, we prove that if F is a totally real field, k is the algebraic closure of the finite field with l elements and r : G_F --> GL_2(k) is irreducible and modular…
Companion forms for unitary and symplectic groups
Toby Gee, David Geraghty
We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a techni…