Toby Gee
Explicit reduction modulo p of certain 2-dimensional crystalline representations, II.
Tue, 04/10/2012 - 15:01 — SomNambulAuthors: Toby Gee, Kevin Buzzard
Subjects: Number Theory
AbstractWe complete the calculations begun in [BG09], using the p-adic local
Langlands correspondence for GL2(Q_p) to give a complete description of the
reduction modulo p of the 2-dimensional crystalline representations of G_{Q_p}
of slope less than 1, when p > 2.The conjectural connections between automorphic representations and Galois representations.
Tue, 09/07/2010 - 15:01 — SomNambulAuthors: Toby Gee, Kevin Buzzard
Subjects: Number Theory
AbstractWe state conjectures on the relationships between automorphic representations
and Galois representations, and give evidence for them.Companion forms for unitary and symplectic groups.
Thu, 01/14/2010 - 16:01 — SomNambulAuthors: Toby Gee, David Geraghty
Subjects: Number Theory
AbstractWe 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 technique for deducing companion forms theorems due to the
first author. We deduce results about the possible Serre weights of mod l
Galois representations corresponding to automorphic representations on unitary
groups. We then use functoriality to prove similar results for automorphic
representations of GSp4 over totally real fields.The Sato-Tate conjecture for Hilbert modular forms.
Tue, 12/08/2009 - 16:01 — SomNambulAuthors: Toby Gee, Thomas Barnet-Lamb, David Geraghty
Subjects: Number Theory
AbstractWe 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 of $\GL_2(\A_F)$, $F$ a totally
real field, which are not of CM type. The argument is based on the potential
automorphy techniques developed by Taylor et. al., but makes use of automorphy
lifting theorems over ramified fields, together with a 'topological' argument
with local deformation rings.Serre weights for quaternion algebras.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Toby Gee, David Savitt
Subjects: Number Theory
AbstractWe study the possible weights of an irreducible two-dimensional mod p
representation of the absolute Galois group of F which is modular in the sense
of that it comes from an automorphic form on a definite quaternion algebra with
centre F which is ramified at all places dividing p, where F is a totally real
field. In most cases we determine the precise list of possible weights; in the
remaining cases we determine the possible weights up to a short and explicit
list of exceptions.Serre weights for quaternion algebras.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Toby Gee, David Savitt
Subjects: Number Theory
AbstractWe study the possible weights of an irreducible two-dimensional mod p
representation of the absolute Galois group of F which is modular in the sense
of that it comes from an automorphic form on a definite quaternion algebra with
centre F which is ramified at all places dividing p, where F is a totally real
field. In most cases we determine the precise list of possible weights; in the
remaining cases we determine the possible weights up to a short and explicit
list of exceptions.
User login
