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9780521596428

Geometric Galois Actions

by
  • ISBN13:

    9780521596428

  • ISBN10:

    0521596424

  • Format: Paperback
  • Copyright: 1997-07-28
  • Publisher: Cambridge University Press

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Supplemental Materials

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Summary

The first of two volumes on anabelian algebraic geometry, this book contains the famous manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. This work, written fourteen years after his retirement from public life in mathematics, includes the closely related letter to Gerd Faltings, published for the first time in this volume. Together these documents describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves. The book is written in an artistic and informal style. It contains several articles on subjects directly related to the ideas explored in the manuscripts, including surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.

Table of Contents

Preface 1(4)
Esquisse d'un Programme
5(44)
Alexandre Grothendieck
Brief an G. Faltings
49(10)
Alexandre Grothendieck
Grothendieck's "Long March through Galois theory"
59(8)
Leila Schneps
The algebraic fundamental group
67(18)
Frans Oort
Etale homotopy type of the moduli spaces of algebraic curves
85(12)
Takayuki Oda
The `obvious' part of Belyi's theorem and Riemann surfaces with many automorphisms
97(16)
Jurgen Wolfart
Glimpses of Grothendieck's anabelian geometry
113(14)
Florian Pop
Some illustrative examples for anabelian geometry in high dimensions
127(12)
Yasutaka Ihara
Hiroaki Nakamura
The fundamental groups at infinity of the moduli spaces of curves
139(20)
Pierre Lochak
Galois representations in the profinite Teichmuller modular groups
159(16)
Hiroaki Nakamura
Deux lettres sur la cohomologie non abelienne
175(8)
Jean-Pierre Serre
The Grothendieck-Teichmuller group GT: a survey
183(22)
Leila Schneps
Approximating Galois orbits of dessins
205(26)
David Harbater
Leila Schneps
Tame and stratified objects
231(12)
Bernard Teissier
Sketch of a Programme (translation into English) 243(42)
Letter to G. Faltings (translation into English) 285

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