Recent developments in the inverse Galois problem : a Joint Summer Research Conference on Recent Developments in the Inverse Galois problem, July 17-23, 1993, University of Washington, Seattle / Michael D. Fried, coordinating editor ; Shreeram S. Abhyankar [and three others], editors.

Format:

Book

Conference/Event

Contributor:

Fried, Michael D., 1942- editor.

Abhyankar, Shreeram Shankar, editor.

American Mathematical Society, issuing body.

Conference Name:

Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem (1993 : Seattle, Wash.), issuing body.

Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem

Series:

Contemporary mathematics (American Mathematical Society) ; 186.

Contemporary mathematics, 0271-4132 ; 186

Language:

English

Subjects (All):

Inverse Galois theory--Congresses.

Inverse Galois theory.

Physical Description:

1 online resource (416 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1995]

Language Note:

English

Summary:

This book contains the refereed proceedings of the AMS-IMS-SIAM 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.

Contents:

""Contents""; ""Preface""; ""Part A: Explicit Quotients of GQ and GF(t)""; ""Explicit Galois realization of C16-extensions of An and Sn""; ""Topics in Galois theory""; ""Parametric solutions of embedding problems""; ""Some projective linear groups over finite fields as Galois groups over Q""; ""K-admissibility of metacyclic 2-groups""; ""Embedding problems and the C16 â?? C8 obstruction""; ""Cyclic covers of P1 and Galois action on their division points""; ""Part B: Moduli Spaces and the Structure of GQ""

""Introduction to modular towers: Generalizing dihedral group-modular curve connections""""On Galois actions on profinite completions of braid groups""; ""On the Galois image in the derivation algebra of π1 of the projective line minus three points""; ""Part C: The Structure of GR(t), GFq(t), and GQp(t)""; ""Covers of P1 over the р-adics""; ""Existence de points p-adiques pour tout p sur un espace de Hurwitz""; ""Stable models""; ""Tout groupe fini est un groupe de Galois sur Qp(T), d'apres Harbater""; ""Specializations of coverings and their Galois groups""

""Rational points and canonical heights on K3-surfaces in P1 x P1 x P1""""Part D: Group Theory and Geometric Monodromy Groups""; ""Mathieu group coverings and linear group coverings""; ""Fundamental groups for arbitrary categories""; ""Monodromy groups of branched coverings: The generic case""; ""Fundamental groups and embedding problems in characteristic p""; ""On free profinite groups of uncountable rank""; ""Primitive monodromy groups of polynomials""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-7777-1

0-8218-5523-9