Deformation of Outer Representations of Galois Group

2004/05/18 by Arash Rastegar, Rastegar, Arash
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #math.NT #math.RT #msc:11G30 #msc:17B10 #msc:17B56 #msc:17B65

paper · pdf · doi:10.48550/arxiv.math/0405351

20 pages, some corrections are implemented in the revised version

arxiv created 2006/09/30 · arxiv updated 2009/12/01

Abstract

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 those coming from deformations of "abelian" Galois representations induced by the Tate module of associated Jacobian variety. We develop an arithmetic deformation theory of graded Lie algebras with finite dimensional graded components to serve our purpose.

Related

• Deformation of Outer Representations of Galois Group II
• Arithmetic Teichmuller Theory
• Arithmetic Deformation Theory of Lie Algebras
• Étale fundamental groups of smooth arithmetic surfaces and the Grothendieck conjecture
• The deformation theory of representations of the fundamental group of a smooth variety