Deformation Rings and Hecke Algebras in the Totally Real Case
نویسندگان
چکیده
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 F . In case of abelian representations, a satisfactory answer is known for compatible system of l-adic representations, and these types of abelian representations are obtained from algebraic Hecke characters. In this paper, we discuss the question for two dimensional representations over a totally real number field.
منابع مشابه
Arithmetic Deformation Theory of Lie Algebras
This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...
متن کاملHecke Algebras and Representations of Finite Reductive Groups
Let F be a eld and G a nite group. Choosing a suitable Mackey system of subfactors of G one can subdivide the irreducible FG-modules into series labelled by semisimple Harish-Chandra vertices and sources. This reduces the classiication problem for irreducible FG-modules partially to the problem of nding the irreducible representations of certain endomorphism rings of Harish-Chandra induced modu...
متن کاملOn Artin Representations and Nearly Ordinary Hecke Algebras over Totally Real Fields
We prove many new cases of the strong Artin conjecture for two-dimensional, totally odd, insoluble (icosahedral) representations Gal(F/F ) → GL2(C) of the absolute Galois group of a totally real field F . 2010 Mathematics Subject Classification: 11G80, 11F33, 11F41, 14G22, 14G35
متن کاملQuantum Drinfeld Hecke Algebras
We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the quantum setting over a field of arbitrary characteristic. We give necessary and sufficient conditions for such algebras to satisfy a Poincaré-Birkhoff-Witt proper...
متن کاملResearch Program
I work on the cohomology, structure, and representations of various types of rings, such as Hopf algebras and group-graded algebras. My research program involves collaborations with many mathematicians, including work with postdocs and graduate students. Below is a summary of some of my past and ongoing research projects, which fall loosely into three categories: Hochschild cohomology and defor...
متن کامل