Deformation rings and Hecke algebras in the totally real case

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.

This is the major update to my deformation ring paper, which is already submitted to a journal

Cited by in corpus (10)

• Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes
• On Ihara's lemma for Hilbert Modular Varieties
• Level optimization in the totally real case
• Minimal modularity lifting for GL2 over an arbitrary number field
• The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in the Hecke algebra
• Universal deformation rings of group representations, with an application of Brauer's generalized decomposition numbers
• Lattices in the cohomology of $U(3)$ arithmetic manifolds
• On the modularity of supersingular elliptic curves over certain totally real number fields
• A deformation problem for Galois representations over imaginary quadratic fields
• Freeness of $p$-adically Completed Modular Jacobians over a Hecke Algebra