Overview

The first of two companion volumes on anabelian algebraic geometry, this book contains the famous, but hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. This work, written in 1984, fourteen years after his retirement from public life in mathematics, together with the closely connected letter to Gerd Faltings, dating from 1983 and also published for the first time in this volume, describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves; it is written in an artistic and informal style. The book also contains several articles on subjects directly related to the ideas explored in the manuscripts; these are surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.

Full Product Details

Author:   Leila Schneps (Centre National de la Recherche Scientifique (CNRS), Paris) ,  Pierre Lochak (Centre National de la Recherche Scientifique (CNRS), Paris)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
Volume:   242
ISBN:  

9780511758874

ISBN 10:   0511758871
Publication Date:   05 April 2013
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   Available To Order  
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Table of Contents

1. Esquisse d'un programme A. Grothendieck; 2. Letter to Faltings A. Grothendieck; 3. The Algebraic fundamental group F. Oort; 4. Grothendieck's 'Long March through Galois Theory' L. Schneps; 5. Survey of the anabelian conjecture F. Pop; 6. Etale homotopy type of the moduli spaces of algebraic curves T. Oda; 7. Tame topology B. Teissier; 8. The obvious part of Belyi's theorem and Riemann surfaces with many automorphisms J. Wolfart; 9. Singularities of moduli spaces, Galois cartography and finite projective geometry V. Adrianov and G. Shabat; 10. π1 of moduli spaces at infinity P. Lochak; 11. Galois actions on higher genus mapping class groups H. Nakamura; 12. On GT L. Schneps; 13. On the GT action on covers D. Harbater and L. Schneps; 14. Two letters on non-abelian cohomology J.-P. Serre.

Reviews

'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 matière à rêver.' Monatshefte für Mathematik

'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 matiere ... rever.' Monatshefte fur Mathematik

'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 matiere a rever.' Monatshefte fur Mathematik

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