Arithmetic Fundamental Groups and Noncommutative Algebra : 1999 Von Neumann Conference on Arithmetic Fundamental Groups and Noncommutative Algebra, August 16-27, 1999, Mathematical Sciences Research I

The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G {\mathbb Q}$ of the algebraic numbers and its close relatives. By analyzing how $G {\mathbb Q}$ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s.