2006/09/30 by Arash Rastegar, Rastegar, Arash
Mathematics · #11G30 (Primary) #17B10 #17B56 #17B65 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11G30 #msc:17B10 #msc:17B56 #msc:17B65
paper · pdf · doi:10.48550/arxiv.math/0610012
8 pages
arxiv created 2006/09/30 · arxiv updated 2009/12/01
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 universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for functors on Artin local rings. In the second part, we use a version of Schlessinger criteria for functors on the Artinian category of nilpotent Lie algebras which is formulated by Pridham, and explore arithmetic applications.