Groupes de Galois arithmétiques et différentiels 1st Edition by Daniel Bertrand, Pierre Dèbes 9782856292228 2856292224
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Product details:
ISBN 10: 2856292224
ISBN 13: 9782856292228
Author: Daniel Bertrand, Pierre Dèbes
On March 8-13, 2004, a meeting was organized at the Luminy CIRM (France) on arithmetic and differential Galois groups, reflecting the growing interactions between the two theories. The present volume collects the proceedings of this conference. It covers the following themes: moduli spaces (of curves, of coverings, of connexions), including the recent developments on modular towers; the arithmetic of coverings and of differential equations (fields of definition, descent theory); fundamental groups; the inverse problems and methods of deformation; and the algorithmic aspects of the theories, with explicit computations or realizations of Galois groups.
Table of contents:
Chapter 1: Algorithms and Moduli Spaces for Differential Equations
Chapter 2: Families of Linear Differential Equations on the Projective Line
Chapter 3: Brief Introduction to Painlevé VI
Chapter 4: Correspondences, Fermat Quotients, and Uniformization
Chapter 5: Jacobiens, Jacobiennes et Stabilité Numérique
Chapter 6: An Introduction to the Modular Tower Program
Chapter 7: Variation of Parabolic Cohomology and Poincaré Duality
Chapter 8: The Main Conjecture of Modular Towers and Its Higher Rank Generalization
Chapter 9: Properties of Lamé Operators with Finite Monodromy
Chapter 10: On the Riemann–Hilbert Problem and Stable Vector Bundles on the Riemann Sphere
Chapter 11: Integral p-Adic Differential Modules
Chapter 12: Galois Theory of Zariski Prime Divisors
Chapter 13: Hurwitz Spaces
Chapter 14: The Group Theory Behind Modular Towers
Chapter 15: Formalized Proof, Computation, and the Construction Problem in Algebraic Geometry
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Tags: Daniel Bertrand, Pierre Dèbes, Groupes, différentiels