Now showing items 1-14 of 14

    • Automorphy for Some \(l\)-Adic Lifts of Automorphic Mod \(l\) Galois Representations 

      Clozel, Laurent; Taylor, Richard; Harris, Michael (Springer Berlin / Heidelberg, 2008)
      We extend the methods of Wiles and of Taylor and Wiles from \(GL_2\) to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), minimally ...
    • Companion Forms and Weight One Forms 

      Buzzard, Kevin; Taylor, Richard L. (Princeton University, 1999)
    • Compatibility of Local and Global Langlands Correspondences 

      Taylor, Richard L.; Yoshida, Teruyoshi (American Mathematical Society, 2007)
      We prove the compatibility of local and global Langlands correspondences for \(GL_n\), which was proved up to semisimplification in M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, ...
    • A Family of Calabi-Yau Varieties and Potential Automorphy 

      Harris, Michael; Shepherd-Barron, Nick; Taylor, Richard L. (Princeton University, 2009)
    • Icosahedral Galois Representations 

      Taylor, Richard L. (Mathematical Sciences Publishers, 1997)
      To the memory of Olga Taussky-Todd
    • Local-global compatibility for l=p, I 

      Barnet-Lamb, Thomas; Gee, Toby; Geraghty, David; Taylor, Richard (Cellule MathDoc/CEDRAM, 2012)
      We prove the compatibility of the local and global Langlands correspondences at places dividing l for the l-adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations ...
    • Modularity of Certain Potentially Barsotti-Tate Galois Representations 

      Conrad, Brian; Diamond, Fred; Taylor, Richard L. (American Mathematical Society, 1999)
      We show that certain potentially semistable lifts of modular modrepresentations are themselves modular. As a result we show that any elliptic curve over the rational numbers with conductor not divisible by 27 is modular.
    • Modularity of some elliptic curves over totally real fields 

      Le hung, Bao Viet (2014-06-06)
      In this thesis, we investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set non-modular j-invariants. By analyzing quadratic points on some modular ...
    • On Icosahedral Artin Representations 

      Buzzard, Kevin; Dickinson, Mark; Shepherd-Barron, Nick I.; Taylor, Richard L. (Duke University Press, 2001)
      If ρ: Gal(Qac/Q) → GL2(C) is a continuous odd irreducible representation with nonsolvable image, then under certain local hypotheses we prove that is the representation associated to a weight 1 modular form and hence ...
    • On Icosahedral Artin Representations, II 

      Taylor, Richard L. (Johns Hopkins University Press, 2003)
      We prove that some new infinite families of odd two dimensional icosahedral representations of the absolute Galois group of Q are modular and hence satsify the Artin conjecture. We also give an account of work of Ramakrishna ...
    • On the Meromorphic Continuation of Degree Two L-Functions 

      Taylor, Richard L. (Universität Bielefeld, Fakultät für Mathematik, 2006)
      We prove that the L-function of any regular (distinct Hodge numbers), irreducible, rank two motive over the rational numbers has meromorphic continuation to the whole complex plane and satisfies the expected functional equation.
    • On the Modularity of Elliptic Curves Over Q: Wild 3-Adic Exercises 

      Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard L. (American Mathematical Society, 2001)
    • Ring-Theoretic Properties of Certain Hecke Algebras 

      Taylor, Richard L.; Wiles, Andrew (Princeton University, 1995)
    • Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations 

      Boxer, George A. (2015-05-18)
      We introduce a method for producing congruences between Hecke eigenclasses, possibly torsion, in the coherent cohomology of automorphic vector bundles on certain good reduction Shimura varieties. The congruences are ...