9 papers
Reduction modulo p of crystalline Galois representations via μ_p-equivariance
Bhargav Bhatt, Toby Gee, Mark Kisin
For a crystalline representation of the absolute Galois group of Q_p, with given Hodge-Tate weights, we obtain new constraints on the inertial weights of its mod p reduction. This…
Prescribed lifts of 2-dimensional representations
Matthew Emerton, Toby Gee, Lue Pan +1
Let F be a totally real field, and let p be prime. Under standard Taylor--Wiles hypotheses, we show that an irreducible, 2-dimensional, totally odd mod p representation of the abso…
The Breuil-Mézard conjecture for potentially Barsotti-Tate representations
Toby Gee, Mark Kisin
We prove the Breuil-Mézard conjecture for 2-dimensional potentially Barsotti-Tate representations of the absolute Galois group G_K, K a finite extension of Q_p, for any p>2 (up to…
A categorical p-adic Langlands correspondence for GL_2(Q_p)
Andrea Dotto, Matthew Emerton, Toby Gee
Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a d…
Localization of smooth p-power torsion representations of GL_2(Q_p)
Andrea Dotto, Matthew Emerton, Toby Gee
We show that the category of smooth representations of GL_2(Q_p) on p-power torsion modules localizes over a certain projective scheme, and give some applications.
Modularity theorems for abelian surfaces
Toby Gee
This is a brief account of my results with George Boxer, Frank Calegari and Vincent Pilloni on the (potential) modularity of abelian surfaces.