Galois-teichmÃœller Theory And Arithmetic Geometry: (63 Advanced Studies in Pure Mathematics)

From the 1980's, Grothendieck's “Esquisse d'un Programme” triggered tremendous developments in number theory and arithmetic geometry, extending from the studies of anabelian geometry and related Galois representations to those of polylogarithms and multiple zeta values, motives, rational points on arithmetic varieties, and effectiveness questions in arithmetic geometry. The present volume collects twenty-four articles written by speakers (and their coauthors) of two international meetings focused on the above themes held in Kyoto in October 2010. It includes both survey articles and research papers which provide useful information about this area of investigation.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

Table of Contents:
Remarks on the Milnor conjecture over schemes by A. Auel On the decomposition of motivic multiple zeta values by F. C. S. Brown Combinatorics of the double shuffle Lie algebra by S. Carr and L. Schneps On the double zeta values by P. Cartier Harmonic Galois theory for finite graphs by S. Corry Twisted covers and specializations by P. Debes and F. Legrand Geometric interpretation of double shuffle relation for multiple $L$-values by H. Furusho Noether's problem for transitive permutation groups of degree $6$ by K. Hashimoto and H. Tsunogai Comparison of some quotients of fundamental groups of algebraic curves over $p$-adic fields by Y. Ihara Dimensions of moduli spaces of finite flat models by N. Imai Results and conjectures in profinite Teichmuller theory by P. Lochak Galois actions on complex braid groups by I. Marin The (local) lifting problem for curves by A. Obus Some remarks on profinite completion of spaces by G. Quick An abelian surface with constrained $3$-power torsion by C. Rasmussen Fake liftings of Galois covers between smooth curves by M. Saidi Motivic aspects of anabelian geometry by A. Schmidt On cuspidal sections of algebraic fundamental groups by J. Stix A note on quadratic residue curves on rational ruled surfaces by H. Tokunaga $n$-nilpotent obstructions to $\pi_1$ sections of $\mathbb P^1 - \{0,1,\infty \}$ and Massey products by K. Wickelgren Lie algebras of Galois representations on fundamental groups by Z. Wojtkowiak $p$-adic multiple zeta values, $p$-adic multiple $L$-values, and motivic Galois groups by G. Yamashita Topics surrounding the combinatorial anabelian geometry of hyperbolic curves I: Inertia groups and profinite Dehn twists by Y. Hoshi and S. Mochizuki Some congruence properties of Eisenstein invariants associated to elliptic curves by H. Nakamura