Now showing items 1-14 of 14

• #### Automorphy for Some $l$-Adic Lifts of Automorphic Mod $l$ Galois Representations ﻿

(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 ﻿

(Princeton University, 1999)
• #### Compatibility of Local and Global Langlands Correspondences ﻿

(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 ﻿

(Princeton University, 2009)
• #### Icosahedral Galois Representations ﻿

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

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(American Mathematical Society, 2001)
• #### Ring-Theoretic Properties of Certain Hecke Algebras ﻿

(Princeton University, 1995)
• #### Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations ﻿

(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 ...