Galois groups over Q : proceedings of a workshop held March 23-27, 1987

Y. Ihara, K. Ribet, J.-P. Serre, editors

This volume is being published in connection with a March, 1987 workshop on Galois groups over Q and related topics, held at the Mathematical Sciences Research Institute in Berkeley. The organizing committee for the workshop consisted of Kenneth Ribet (chairman), Yasutaka Ihara, and Jean-Pierre Serre. The volume contains key original papers by experts in the field, and treats a variety of questions in arithmetical algebraic geometry. A number of the contributions discuss Galois actions on fundamental groups, and associated topics: these include Fermat curves, Gauss sums, cyclotomic units, and motivic questions. Other themes which reoccur include semistable reduction of algebraic varieties, deformations of Galois representations, and connections between Galois representations and modular forms. The authors contributing to the volume are: G.W. Anderson, D. Blasius, D. Ramakrishnan, P. Deligne, Y. Ihara, U. Jannsen, B.H. Matzat, B. Maszur, and K. Wingberg. The contributions are of exceptionally high quality, and this book will have permanent value. The volume will be of great interest to students and established workers in many areas of algebraic number theory and algebraic geometry.

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[目次]

  • 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.Geometrie algebrique dans une categorie tannakienne.- 6.Le groupe fondamental d'une categorie tannakienne.- 7.Geometrie algebrique dans la categorie tannakienne des systemes de realisations: interpretations.- 8.Extensions iterees de motifs de Tate.- 9.Rappels sur les groupes unipotents.- 10.Theories du ?1.- Groupoides.- Theorie classique.- Theorie profinie.- Theorie algebrique.- 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 a l'infini.- Theorie classique.- Theorie profinie.- Theorie algebrique.- Compatibilites.- Theorie motivique.- 16.P1 moins trois points: un quotient de ?1 motivique.- 17.Relations de distribution: voie geometrique.- 18.Le torseur Pd.k + ( ? 1 )k ? Pd.k est de torsion: voie geometrique.- 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 and discussion.- 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.- 1.1Deformations.- 1.2Existence of universal deformation rings.- 1.3Functoriality.- 1.4One-dimensional representations.- 1.5The duality involution.- 1.6Obstructions.- 1.7Ordinary representations.- 1.8Schur-type results.- 1.9A few simple examples.- 1.10 Global Galois representations.- 1.11Remarks on Galois representations to SL2(Fp).- 1.12Neat residual representations.- 1.13Neat S3-extensions of ?.- 2.The internal structure of universal deformation spaces.- 2.1General glossary.- 2.2Special dihedral representations.- 2.3The origin.- 2.4The globally dihedral locus.- 2.5The ordinary locus.- 2.6The inertially reducible locus.- 2.7The inertially metabelian and the inertially dihedral locus.- 2.8Loci of constant p-adic Hodge type.- Galois Groups of Poincare 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.

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この本の情報

書名 Galois groups over Q : proceedings of a workshop held March 23-27, 1987
著作者等 Mathematical Sciences Research Institute
Ribet, Kenneth A.
Serre, Jean Pierre
Workshop on "Galois Groups over Q and Related Topics"
伊原 康隆
Ribet Kenneth
Serre J.P.
Ihara Y.
シリーズ名 Mathematical Sciences Research Institute publications
出版元 Springer-Verlag
刊行年月 c1989
版表示 Softcover reprint of the original 1st ed. 1989
ページ数 x, 449 p.
大きさ 25 cm
ISBN 3540970312
9781461396512
NCID BA07252355
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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