Galois Groups over ?

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.