Galois Groups over Q: Proceedings of a Workshop Held March 23-27, 1987 (Mathematical Sciences Research Institute Publications)

This volume is being published in connection with a March, 1987 workshop on Galois groups over Q and related topics, held at the Mathematical Sciences Research Institute in Berkeley. The organizing committee for the workshop consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and Jean-Pierre Serre. The volume contains key original papers by experts in the field, and treats a variety of questions in arithmetical algebraic geometry. A number of the contributions discuss Galois actions on fundamental groups, and associated topics: these include Fermat curves, Gauss sums, cyclotomic units, and motivic questions. Other themes which reoccur include semistable reduction of algebraic varieties, deformations of Galois representations, and connections between Galois representations and modular forms. The authors contributing to the volume are: G.W. Anderson, D. Blasius, D. Ramakrishnan, P. Deligne, Y. Ihara, U. Jannsen, B.H. Matzat, B. Maszur, and K. Wingberg. The contributions are of exceptionally high quality, and this book will have permanent value. The volume will be of great interest to students and established workers in many areas of algebraic number theory and algebraic geometry. 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 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. Y. Ihara, K. Ribet, J.p. Serre, Editors. Workshop Held At The Mathematical Sciences Research Institute. Includes Bibliographical References.