Galois Groups over ? : Proceedings of a Workshop Held March 23–27, 1987 (Softcover reprint of the original 1st ed. 1989)

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.