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El. knyga: Geometric Galois Actions: Volume 1, Around Grothendieck's Esquisse d'un Programme

Edited by (Centre National de la Recherche Scientifique (CNRS), Paris), Edited by (Centre National de la Recherche Scientifique (CNRS), Paris)
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Contains Grothendieck's previously unpublished manuscript 'Esquisse d'un Programme' and related papers.

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.

Recenzijos

'These two volumes, containing both gentle introductions and research papers dealing with various aspects of Grothendieck's Esquisse, represent not only invaluable resources but also matičre ą rźver.' Monatshefte für Mathematik

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Contains Grothendieck's previously unpublished manuscript 'Esquisse d'un Programme' and related papers.
Preface 1(4) Esquisse dun Programme 5(44) Alexandre Grothendieck Brief an G. Faltings 49(10) Alexandre Grothendieck Grothendiecks 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 Belyis theorem and Riemann surfaces with many automorphisms 97(16) Jurgen Wolfart Glimpses of Grothendiecks 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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