Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Ii
Download Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Ii PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Topics Surrounding The Combinatorial Anabelian Geometry Of Hyperbolic Curves Ii book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II
The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero. The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space. We then turn to the study of tripod synchronization, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve induces the same outer automorphism on certain subquotients of such a fundamental group determined by tripods [i.e., copies of the projective line minus three points]. The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists. In the final portion of the monograph, we develop a theory of localizability, on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space. This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the étale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
Arithmetic and Geometry Around Galois Theory
Author: Pierre Dèbes
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-13
This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.
Current Developments in Algebraic Geometry
Author: Lucia Caporaso
language: en
Publisher: Cambridge University Press
Release Date: 2012-03-19
This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.