Deformation of Outer Representations of Galois Group II

Details Deformation of Outer Representations of Galois Group II Deformation of Outer Representations of Galois Group II

2006-09-30

arxiv.org/abs/math/0610012v1

Mathematics

Number Theory

8 pages

Scientific paper

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.

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