  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.
