TY - JOUR T1 - Deformation of Outer Representations of Galois Group II TT - JF - IJMSI JO - IJMSI VL - 6 IS - 2 UR - http://ijmsi.ir/article-1-235-en.html Y1 - 2011 SP - 33 EP - 41 KW - Deformation theory KW - Artin local rings KW - Schlessinger criteria. N2 - 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 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. M3 10.7508/ijmsi.2011.02.004 ER -