Eight expository articles by well-known authors of the theory of Galois groups and fundamental groups focus on recent developments, avoiding classical aspects which have already been described at length in the standard literature. The volume grew from the special semester held at the MSRI in Berkeley in 1999 and many of the new results are due to work accomplished during that program. Among the subjects covered are elliptic surfaces, Grothendieck's anabelian conjecture, fundamental groups of curves and differential Galois theory in positive characteristic. Although the articles contain original results, the authors have striven to make them as introductory as possible, making them accessible to graduate students as well as researchers in algebraic geometry and number theory. The volume also contains a lengthy overview by Leila Schneps that sets the individual articles into the broader context of contemporary research in Galois groups.
Author(s): Leila Schneps
Series: Mathematical Sciences Research Institute Publications
Publisher: Cambridge University Press
Year: 2003
Language: English
Pages: 482
Galois Groups and Fundamental Groups......Page 1
Mathematical Sciences Research Institute Publications......Page 4
Table of Contents......Page 7
Introduction......Page 8
Monodromy Groups of Coverings of Curves......Page 14
On the Tame Fundamental Groups of Curves over Algebraically Closed Fields of Characteristic......Page 60
On the Specialization Homomorphism of Fundamental Groups of Curves in Positive Characteristic......Page 119
Topics Surrounding the Anabelian Geometry
of Hyperbolic Curves......Page 132
Monodromy of Elliptic Surfaces......Page 180
Tannakian Fundamental GroupsAssociated to Galois Groups......Page 196
Special Loci in Moduli Spaces of Curves......Page 230
Cellulation of Compactified Hurwitz Spaces......Page 290
Patching and Galois Theory......Page 326
Constructive Differential Galois Theory......Page 438
