Advanced Studies in Pure Mathematics 2012; 832 pp; hardcover Volume: 63 ISBN10: 4864970149 ISBN13: 9784864970143 List Price: US$148 Member Price: US$118.40 Order Code: ASPM/63
 Since the 1980s, Grothendieck's "Esquisse d'un Programme" has 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. This volume contains twentyfour articles based on talks presented at two international meetings that focused on the above themes. The meetings were held in Kyoto in October 2010. The volume includes both survey articles and research papers that provide useful information about this area of investigation. Volumes in this series are freely available electronically 5 years postpublication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership Graduate students and research mathematicians interested in GaloisTeichmüller theory and arithmetic geometry. Table of Contents  A. Auel  Remarks on the Milnor conjecture over schemes
 F. C. S. Brown  On the decomposition of motivic multiple zeta values
 S. Carr and L. Schneps  Combinatorics of the double shuffle Lie algebra
 P. Cartier  On the double zeta values
 S. Corry  Harmonic Galois theory for finite graphs
 P. Dèbes and F. Legrand  Twisted covers and specializations
 H. Furusho  Geometric interpretation of double shuffle relation for multiple \(L\)values
 K. Hashimoto and H. Tsunogai  Noether's problem for transitive permutation groups of degree \(6\)
 Y. Ihara  Comparison of some quotients of fundamental groups of algebraic curves over \(p\)adic fields
 N. Imai  Dimensions of moduli spaces of finite flat models
 P. Lochak  Results and conjectures in profinite Teichmüller theory
 I. Marin  Galois actions on complex braid groups
 A. Obus  The (local) lifting problem for curves
 G. Quick  Some remarks on profinite completion of spaces
 C. Rasmussen  An abelian surface with constrained \(3\)power torsion
 M. Saïdi  Fake liftings of Galois covers between smooth curves
 A. Schmidt  Motivic aspects of anabelian geometry
 J. Stix  On cuspidal sections of algebraic fundamental groups
 H. Tokunaga  A note on quadratic residue curves on rational ruled surfaces
 K. Wickelgren  \(n\)nilpotent obstructions to \(\pi_1\) sections of \(\mathbb P^1  \{0,1,\infty \}\) and Massey products
 Z. Wojtkowiak  Lie algebras of Galois representations on fundamental groups
 G. Yamashita  \(p\)adic multiple zeta values, \(p\)adic multiple \(L\)values, and motivic Galois groups
 Y. Hoshi and S. Mochizuki  Topics surrounding the combinatorial anabelian geometry of hyperbolic curves I: Inertia groups and profinite Dehn twists
 H. Nakamura  Some congruence properties of Eisenstein invariants associated to elliptic curves
