Deformation rings and Hecke algebras in the totally real case

TL;DR

This paper investigates the relationship between deformation rings and Hecke algebras for two-dimensional Galois representations over totally real fields, advancing understanding in number theory's fundamental questions.

Contribution

It explores the structure of deformation rings and their connection to Hecke algebras in the context of totally real fields, providing new insights into Galois representations.

Findings

Established links between deformation rings and Hecke algebras

Characterized semi-simple l-adic Galois representations over totally real fields

Contributed to the understanding of number field Galois representations

Abstract

One of the basic questions in number theory is to determine semi-simple l-adic representations of the absolute Galois group of a number field. In this paper, we discuss the question for two dimensional representations over a totally real number field.