Add to ORKGWe prove modularity of some two dimensional 2-adic Galois representations over a totally real field that are nearly ordinary at all places above 2 and that are residually dihedral. We do this by employing the strategy of Skinner and Wiles using Hida families together with the 2-adic patching method of Khare and Wintenberger. As an application we deduce modularity of some elliptic curves over totally real fields that have good ordinary or multiplicative reduction at places above 2
This thesis is about arithmetic, analytic and algorithmic aspects of modular curves and modular form...
For an odd rational prime p and integer n>1, we consider certain continuous representations rho_n of...
The following theorem is well known to experts. Theorem 0.1. Let E an elliptic curve over a totally ...
We establish the automorphy of some families of 2-dimensional representations of the absolute Galois...
We prove that, under some mild conditions, a two dimensional p-adic Galois representation which is r...
We establish the automorphy of some families of 2-dimensional representations of the absolute Galois...
AbstractWe study generalisations to totally real fields of the methods originating with Wiles and Ta...
Abstract. We give a classification of all possible 2-adic images of Galois representations associate...
We present an algorithm to determine if the $L$-series associated to an automorphic representation a...
Throughout this thesis, we develop theory and the algorithms that lead to an effective method to stu...
We prove a modularity lifting theorem for two dimensional, 2-adic, potentially Barsotti-Tate represe...
Let $F$ be a CM number field. We prove modularity lifting theorems forregular $n$-dimensional Galois...
We prove a control theorem for Hida’s ordinary Hecke algebra for the primep= 2,thereby establishing ...
We develop a new strategy for studying low weight specializations of p-adic families of ordinary mod...
This paper is devoted to the proof of two results. The first was conjectured in 1994 by the author. ...
This thesis is about arithmetic, analytic and algorithmic aspects of modular curves and modular form...
For an odd rational prime p and integer n>1, we consider certain continuous representations rho_n of...
The following theorem is well known to experts. Theorem 0.1. Let E an elliptic curve over a totally ...
We establish the automorphy of some families of 2-dimensional representations of the absolute Galois...
We prove that, under some mild conditions, a two dimensional p-adic Galois representation which is r...
We establish the automorphy of some families of 2-dimensional representations of the absolute Galois...
AbstractWe study generalisations to totally real fields of the methods originating with Wiles and Ta...
Abstract. We give a classification of all possible 2-adic images of Galois representations associate...
We present an algorithm to determine if the $L$-series associated to an automorphic representation a...
Throughout this thesis, we develop theory and the algorithms that lead to an effective method to stu...
We prove a modularity lifting theorem for two dimensional, 2-adic, potentially Barsotti-Tate represe...
Let $F$ be a CM number field. We prove modularity lifting theorems forregular $n$-dimensional Galois...
We prove a control theorem for Hida’s ordinary Hecke algebra for the primep= 2,thereby establishing ...
We develop a new strategy for studying low weight specializations of p-adic families of ordinary mod...
This paper is devoted to the proof of two results. The first was conjectured in 1994 by the author. ...
This thesis is about arithmetic, analytic and algorithmic aspects of modular curves and modular form...
For an odd rational prime p and integer n>1, we consider certain continuous representations rho_n of...
The following theorem is well known to experts. Theorem 0.1. Let E an elliptic curve over a totally ...