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Fred Diamond

  1. On Serre's conjecture for mod l Galois representations over totally real fields.

    Чт, 01/07/2010 - 16:01 — SomNambul
    Authors: Fred Diamond, Kevin Buzzard, Frazer Jarvis
    Subjects: Number Theory
    Abstract

    In 1987 Serre conjectured that any mod l ("ell", not "1") two-dimensional
    irreducible odd representation of the absolute Galois group of the rationals
    came from a modular form in a precise way. We present a generalisation of this
    conjecture to 2-dimensional representations of the absolute Galois group of a
    totally real field where l is unramified. The hard work is in formulating an
    analogue of the "weight" part of Serre's conjecture. Serre furthermore asked
    whether his conjecture could be rephrased in terms of a "mod l Langlands
    philosophy".

  2. Extensions of rank one (phi, Gamma)-modules and crystalline representations.

    Ср, 10/14/2009 - 11:03 — SomNambul
    Authors: Seunghwan Chang, Fred Diamond
    Subjects: Number Theory
    Abstract

    Let K be a finite unramified extension of Q_p. We parametrize the (phi,
    Gamma)-modules corresponding to reducible two-dimensional mod p representations
    of G_K and characterize those which have reducible crystalline lifts with
    certain Hodge-Tate weights.

  3. Extensions of rank one (phi, Gamma)-modules and crystalline representations.

    Ср, 10/14/2009 - 11:03 — SomNambul
    Authors: Seunghwan Chang, Fred Diamond
    Subjects: Number Theory
    Abstract

    Let K be a finite unramified extension of Q_p. We parametrize the (phi,
    Gamma)-modules corresponding to reducible two-dimensional mod p representations
    of G_K and characterize those which have reducible crystalline lifts with
    certain Hodge-Tate weights.

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