Weighted Completion of Galois Groups and Galois Actions on the Fundamental Group of P^1  {0,1,infinity}
Abstract
This is a revision of the paper that was previously entitled "Weighted Completion of Galois Groups and Some Conjectures of Deligne". Fix a prime number $ł$. We prove a conjecture stated by Ihara, which he attributes to Deligne, about the action of the absolute Galois group on the pro$ł$ completion of the fundamental group of the thrice punctured projective line. Similar techniques are also used to prove part of a conjecture of Goncharov, also about the action of the absolute Galois group on the fundamental group of the thrice punctured projective line. The main technical tool is the weighted completion of a profinite group with respect to a reductive representation (and other appropriate data). This theory is developed in this paper.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2000
 arXiv:
 arXiv:math/0006158
 Bibcode:
 2000math......6158H
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology;
 Mathematics  Number Theory
 EPrint:
 41 pages, amslatex