Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference
The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen­ tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp­ son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory'). What are the implications for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).
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Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference
The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen­ tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp­ son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory'). What are the implications for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).
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Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference

Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference

Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference

Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference

Overview

The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen­ tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp­ son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory'). What are the implications for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).

Product Details

ISBN-13: 9781441936349
Publisher: Springer US
Publication date: 12/06/2010
Series: Developments in Mathematics , #12
Edition description: Softcover reprint of hardcover 1st ed. 2005
Pages: 168
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Supplementary Thoughts on Symplectic Groups.- Automorphisms of the Modular Curve.- Reducing the Fontaine-Mazur Conjecture to Group Theory.- Relating Two Genus 0 Problems of John Thompson.- Relatively Projective Groups as Absolute Galois Groups.- Invariants of Binary Forms.- Some Classical Views on the Parameters of the Grothendieck-Teichmüller Group.- The Image of a Hurwitz Space Under the Moduli Map.- Very Simple Representations: Variations on a Theme of Clifford.
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