Browsing by Author "Taylor, Richard L."
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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 selfdual, regular (de Rham with distinct HodgeTate 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 CalabiYau Varieties and Potential Automorphy
Harris, Michael; ShepherdBarron, Nick; Taylor, Richard L. (Princeton University, 2009) 
Icosahedral Galois Representations
Taylor, Richard L. (Mathematical Sciences Publishers, 1997)To the memory of Olga TausskyTodd 
Localglobal compatibility for l=p, I
BarnetLamb, 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 ladic Galois representations associated to regular algebraic conjugate selfdual cuspidal automorphic representations ... 
Modularity of Certain Potentially BarsottiTate 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 (20140606)In this thesis, we investigate modularity of elliptic curves over a general totally real number field, establishing a finiteness result for the set nonmodular jinvariants. By analyzing quadratic points on some modular ... 
On Icosahedral Artin Representations
Buzzard, Kevin; Dickinson, Mark; ShepherdBarron, 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 LFunctions
Taylor, Richard L. (Universität Bielefeld, Fakultät für Mathematik, 2006)We prove that the Lfunction 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 3Adic Exercises
Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard L. (American Mathematical Society, 2001) 
RingTheoretic 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. (20150518)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 ...