Galois Groups over ?

This volume is the offspring of a week-long workshop on "e;Galois groups over Q and related topics,"e; 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: "e;Gauss sums, circular units and the simplex"e; * G. Anderson and Y. Ihara: "e;Galois actions on 11"e;1 ( *** ) and higher circular units"e; * D. Blasius: "e;Maass forms and Galois representations"e; * P. Deligne: "e;Galois action on 1I"e;1(P-{0, 1, oo}) and Hodge analogue"e; * W. Feit: "e;Some Galois groups over number fields"e; * Y. Ihara: "e;Arithmetic aspect of Galois actions on 1I"e;1(P - {O, 1, oo})"e; - survey talk * U. Jannsen: "e;Galois cohomology of i-adic representations"e; * B. Matzat: - "e;Rationality criteria for Galois extensions"e; - "e;How to construct polynomials with Galois group Mll over Q"e; * B. Mazur: "e;Deforming GL(2) Galois representations"e; * K. Ribet: "e;Lowering the level of modular representations of Gal( Q/ Q)"e; * J-P. Serre: - Introductory Lecture - "e;Degree 2 modular representations of Gal(Q/Q)"e; * J.