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TitleGalois Groups over โ{132}{154} [electronic resource] : Proceedings of a Workshop Held March 23-27, 1987 / edited by Y. Ihara, K. Ribet, J.-P. Serre
ImprintNew York, NY : Springer US, 1989
Connect tohttp://dx.doi.org/10.1007/978-1-4613-9649-9
Descript X, 449p. 11 illus. online resource

SUMMARY

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: โ{128}ข G. Anderson: "Gauss sums, circular units and the simplex" โ{128}ข G. Anderson and Y. Ihara: "Galois actions on 11"1 ( โ{128}ขโ{128}ขโ{128}ข ) and higher circular units" โ{128}ข D. Blasius: "Maass forms and Galois representations" โ{128}ข P. Deligne: "Galois action on 1I"1(P-{0, 1, oo}) and Hodge analogue" โ{128}ข W. Feit: "Some Galois groups over number fields" โ{128}ข Y. Ihara: "Arithmetic aspect of Galois actions on 1I"1(P - {O, 1, oo})" - survey talk โ{128}ข U. Jannsen: "Galois cohomology of i-adic representations" โ{128}ข B. Matzat: - "Rationality criteria for Galois extensions" - "How to construct polynomials with Galois group Mll over Q" โ{128}ข B. Mazur: "Deforming GL(2) Galois representations" โ{128}ข K. Ribet: "Lowering the level of modular representations of Gal( Q/ Q)" โ{128}ข J-P. Serre: - Introductory Lecture - "Degree 2 modular representations of Gal(Q/Q)" โ{128}ข J


CONTENT

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.Gรฉomรฉtrie algรฉbrique dans une catรฉgorie tannakienne -- 6.Le groupe fondamental dโ{128}{153}une catรฉgorie tannakienne -- 7.Gรฉomรฉtrie algรฉbrique dans la catรฉgorie tannakienne des systรจmes de rรฉalisations: interprรฉtations -- 8.Extensions itรฉrรฉes de motifs de Tate -- 9.Rappels sur les groupes unipotents -- 10.Thรฉories 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 ร  lโ{128}{153}infini -- 16.P1 moins trois points: un quotient de ?1 motivique -- 17.Relations de distribution: voie gรฉomรฉtrique -- 18.Le torseur Pd.k + ( ? 1 )k ? Pd.k est de torsion: voie gรฉomรฉtrique -- 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 -- 2.The internal structure of universal deformation spaces -- Galois Groups of Poincarรฉ 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


Mathematics Group theory Number theory Mathematics Group Theory and Generalizations Number Theory



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