Overview

"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."

Full Product Details

Author:   Y. Ihara ,  Kenneth Ribet ,  J-P. Serre
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1989
Volume:   16
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.698kg
ISBN:  

9781461396512

ISBN 10:   1461396514
Pages:   449
Publication Date:   21 December 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Normalization of the Hyperadelic Gamma Function.- 1.Gaussian units.- 2.The structure of Mr,?.- 3.Normalization.- Maass Forms and Galois Representations.- 1.Automorphic forms via representations.- 2.Holomorphic automorphic forms for GSp(4).- 3.Geometric automorphic forms.- 4.Reductions.- 5.Heuristics and conjectures.- 6.Transfer of problem to GSp(4, A?).- 7.Hypothesis 1: structure of global L-packets for GSp(4).- 8.An analytic estimate for the conjugates of Maass forms.- 9.Hypothesis 2: Galois representations attached to Siegel modular forms of higher weight.- 10.The main theorem.- Le Groupe Fondamental De La Droite Projective Moins Trois Points.- 0.Terminologie et notations.- 1.Motifs mixtes.- 2.Exemples.- 3.Torseurs sous Z(n).- 4.Rappels sur les Ind-objets.- 5.Géométrie algébrique dans une catégorie tannakienne.- 6.Le groupe fondamental d’une catégorie tannakienne.- 7.Géométrie algébrique dans la catégorie tannakienne des systèmes de réalisations: interprétations.- 8.Extensions itérées de motifs de Tate.- 9.Rappels sur les groupes unipotents.- 10.Théories du ?1.- 11.Le Frobenius cristallin du ?1 de Rham.- 12.La filtration de Hodge du ?1.- 13.Le ?1 motivique.- 14.Exemple: le ?1 motivique de Gm.- 15.Points bases à l’infini.- 16.P1 moins trois points: un quotient de ?1 motivique.- 17.Relations de distribution: voie géométrique.- 18.Le torseur Pd.k + ( ? 1 )k ? Pd.k est de torsion: voie géométrique.- 19.Comparaison des Z(h)-torseurs des paragraphes 3 et 16.- Index des notations.- The Galois Representation Arising from P1 ? {0, 1,?} and Tate Twists of Even Degree.- 1.Preliminaries and statement of the Theorem.- 2.Reducing the proof of the Theorem to two key lemmas.- 3.Proof of Key Lemma A.- 4.Proof of Key Lemma B.- 5.Remarks anddiscussion.- On the ?-Adic Cohomology of Varieties Over Number Fields and its Galois Cohomology.- 1.The basic conjecture.- 2.Connections with algebraic K-theory.- 3.Connections with Iwasawa theory.- 4.Global results.- 5.The local case.- 6.The case n ? i + 1 ? 2n.- 7.The case i = 1: abelian varieties.- Rationality Criteria for Galois Extensions.- 1.Fundamental groups.- 2.Class numbers of generators.- 3.Topological automorphisms.- 4.Braids.- 5.Braids and topological automorphisms together.- Deforming Galois Representations.- 1Universal deformation of representations.- 2.The internal structure of universal deformation spaces.- Galois Groups of Poincaré Type Over Algebraic Number Fields.- 1.The function field case.- 2.Classification of Demuskin groups.- 3.p-adic number fields.- 4.n-local fields.- 5.The absolute Galois group of a p-adic number field.- 6.Global number fields.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions