Contemporary Mathematics 1995; 401 pp; softcover Volume: 186 ISBN10: 0821802992 ISBN13: 9780821802991 List Price: US$83 Member Price: US$66.40 Order Code: CONM/186
 This book contains the refereed proceedings of the AMSIMSSIAM Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem, held in July 1993 at the University of Washington, Seattle. A new review of Serre's Topics in Galois Theory serves as a starting point. The book describes the latest research on explicit presentation of the absolute Galois group of the rationals. Containing the first appearance of generalizations of modular curves, the book presents applications that demonstrate the full scope of the Inverse Galois Problem. In particular, the papers collected here show the ubiquity of the applications of the Inverse Galois Problem and its compelling significance. The book will serve as a guide to progress on the Inverse Galois Problem and as an aid in using this work in other areas of mathematics. This includes coding theory and other finite field applications. Group theory and a first course in algebraic curves are sufficient for understanding many papers in the volume. Graduate students will find this an excellent reference to current research, as it contains a list of problems appropriate for thesis material in arithmetic geometry, algebraic number theory, and group theory. Readership Researchers in number theory and group theory and students seeking applications of pure mathematics as downtoearth problems. Table of Contents Part A. Explicit quotients of \(G_{\mathbb Q}\) and \(G_{\bar {\mathbb F}(t)}\)  T. Crespo  Explicit Galois realization of \(C_{16}\)extensions of \(A_n\) and \(S_n\)
 M. D. Fried  Topics in Galois theory
 B. H. Matzat  Parametric solutions of embedding problems
 A. Reverter and N. Vila  Some projective linear groups over finite fields as Galois groups over \(\mathbb Q\)
 S. Liedahl and J. Sonn  \(K\)Admissibility of metacyclic \(2\)groups
 J. R. Swallow  Embedding problems and the \(C_{16}\rightarrow C_8\) obstruction
 H. Völklein  Cyclic covers of \(\mathbb P^1\) and Galois action on their division points
Part B. Moduli spaces and the structure of \(G_{\mathbb Q}\)  M. D. Fried  Introduction to modular towers: Generalizing dihedral groupmodular curve connections
 Y. Ihara and M. Matsumoto  On Galois actions on profinite completions of braid groups
 M. Matsumoto  On the Galois image in the derivation algebra of \(\pi _1\) of the projective line minus three points
Part C. The structure of \(G_{\mathbb R(t)}, G_{\bar {\mathbb F}_q(t)}\), and \(G_{\mathbb Q_p(t)}\)  P. Dèbes  Covers of \(\mathbb P^1\) over the \(p\)adics
 B. Deschamps  Existence de points \(p\)adiques pour tout \(p\) sur un espace de Hurwitz
 E. Dew  Stable models
 Q. Liu  Tout groupe fini est un groupe de Galois sur \(\mathbb Q_p(T)\), d'après Harbater
 W. K. Seiler  Specializations of coverings and their Galois groups
 L. Wang  Rational points and canonical heights on K3surfaces in \(\mathbb P^1\times \mathbb P^1\times \mathbb P^1\)
Part D. Group theory and geometric monodromy groups  S. S. Abhyankar  Mathieu group coverings and linear group coverings
 P. Feit  Fundamental groups for arbitrary categories
 R. M. Guralnick and M. G. Neubauer  Monodromy groups of branched coverings: The generic case
 D. Harbater  Fundamental groups and embedding problems in characteristic \(p\)
 M. Jarden  On free profinite groups of uncountable rank
 P. Müller  Primitive monodromy groups of polynomials
