Galois Groups over ?

1. Front Matter

   Pages i-x

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2. Normalization of the Hyperadelic Gamma Function

   • Greg W. Anderson

   Pages 1-31

3. Maass Forms and Galois Representations

   • Don Blasius, Dinakar Ramakrishnan

   Pages 33-77

4. Le Groupe Fondamental de la Droite Projective Moins Trois Points

   • Par P. Deligne

   Pages 79-297

5. The Galois representation arising from P1 − {0,1, ∞} and Tate twists of even degree

   • Yasutaka Ihara

   Pages 299-313

6. On the ℓ-adic cohomology of varieties over number fields and its Galois cohomology

   • Uwe Jannsen

   Pages 315-360

7. Rationality Criteria for Galois Extensions

   • B. Heinrich Matzat

   Pages 361-383

8. Deforming Galois Representations

   • B. Mazur

   Pages 385-437

9. Galois Groups of Poincaré-Type over Algebraic Number Fields

   • Kay Wingberg

   Pages 439-449

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.

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

• Faculty of Science, Department of Mathematics, Hongo, Tokyo 113, Japan

  Y. Ihara

• Department of Mathematics, University of California at Berkeley, Berkeley, USA

  K. Ribet

• Mathematical Sciences Research Institute, Berkeley, USA

  K. Ribet

• College de France, Paris, France

  J.-P. Serre

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