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Progress in Galois Theory

Proceedings of John Thompson's 70th Birthday Conference

  • Conference proceedings
  • © 2005

Overview

Editors:
  1. Helmut Voelklein

    1. University of Florida, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Tanush Shaska

    1. University of Idaho, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Contains recent results in this classical and elegant area of mathematics
  • Most of the authors are first class mathematicians with a wide reputation
  • Includes supplementary material: sn.pub/extras

Part of the book series: Developments in Mathematics (DEVM, volume 12)

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Table of contents (9 papers)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Supplementary Thoughts on Symplectic Groups

    • Shreeram S. Abhyankar, Nicholas F. J. Inglis, Umud D. Yalcin
    Pages 1-23

  3. Automorphisms of the Modular Curve

    • Peter Bending, Alan Camina, Robert Guralnick
    Pages 25-37

  4. Reducing the Fontaine-Mazur Conjecture to Group Theory

    • Nigel Boston
    Pages 39-50

  5. Relating Two Genus 0 Problems of John Thompson

    • Michael D. Fried
    Pages 51-85

  6. Relatively Projective Groups as Absolute Galois Groups

    • Dan Haran, Moshe Jarden
    Pages 87-100

  7. Invariants of Binary Forms

    • Vishwanath Krishnamoorthy, Tanush Shaska, Helmut Völklein
    Pages 101-122

  8. Some Classical Views on the Parameters of the Grothendieck-Teichmüller Group

    • Hiroaki Nakamura
    Pages 123-133

  9. The Image of a Hurwitz Space Under the Moduli Map

    • Helmut Völklein
    Pages 135-150

  10. Very Simple Representations: Variations on a Theme of Clifford

    • Yuri G. Zarhin
    Pages 151-168
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Keywords

About this book

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 implica­ tions 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).

Editors and Affiliations

  • University of Florida, USA

    Helmut Voelklein

  • University of Idaho, USA

    Tanush Shaska

Bibliographic Information

  • Book Title: Progress in Galois Theory

  • Book Subtitle: Proceedings of John Thompson's 70th Birthday Conference

  • Editors: Helmut Voelklein, Tanush Shaska

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/b101762

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag US 2005

  • Hardcover ISBN: 978-0-387-23533-2Published: 19 November 2004

  • Softcover ISBN: 978-1-4419-3634-9Published: 06 December 2010

  • eBook ISBN: 978-0-387-23534-9Published: 10 August 2006

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: X, 168

  • Topics: Algebra, Group Theory and Generalizations, Algebraic Geometry

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