Framed Deformation of Galois Representation
نویسنده
چکیده
We studied framed deformations of two dimensional Galois representation of which the residue representation restrict to decomposition groups are scalars, and established a modular lifting theorem for certain cases. We then proved a family version of the result, and used it to determine the structure of deformation rings over characteristic zero fields. As a corollary, we obtain the L-invariant of adjoint square representation associated to a Hilbert Hecke eigenform.
منابع مشابه
Deformation of Outer Representations of Galois Group
To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...
متن کاملDeformation of Outer Representations of Galois Group II
This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...
متن کاملDeformations of Polarized Automorphic Galois Representations and Adjoint Selmer Groups
We prove the vanishing of the geometric Bloch–Kato Selmer group for the adjoint representation of a Galois representation associated to regular algebraic polarized cuspidal automorphic representations under an assumption on the residual image. Using this, we deduce that the localization and completion of a certain universal deformation ring for the residual representation at the characteristic ...
متن کاملReview of Galois Deformations
We'll review the study of Galois deformations. Here's the setup. Let G be a pro nite group, and let ρ : G→ GLn(k) be a representation of G over a nite eld k of characteristic p. Let Λ be a complete DVR with residue eld k, and let CΛ denote the category whose objects are artinian local Λ-algebras with residue eld k, and whose morphisms are local homomorphisms. Let ĈΛ denote the category of compl...
متن کاملFiniteness of Unramified Deformation Rings
We prove that the universal unramified deformation ring R of a continuous Galois representation ρ : GF+ → GLn(k) (for a totally real field F and finite field k) is finite over O = W (k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring R is finite over the local deformation ring R.
متن کامل