2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117762This 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.8 pagesNumber TheoryRepresentation Theory11G30 (Primary); 17B10; 17B56; 17B65 (Secondary)text