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

Contains Grothendieck's previously unpublished manuscript 'Esquisse d'un Programme' and related papers.

Leila Schneps (Edited by), Pierre Lochak (Edited by)

9780521596428, Cambridge University Press

Paperback, published 10 July 1997

304 pages, 1 b/w illus.
22.9 x 15.3 x 2 cm, 0.502 kg

'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

The first of two companion volumes on anabelian algebraic geometry, this book contains the famous, but hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck.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.

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. ?1 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.

Subject Areas: Combinatorics & graph theory [PBV]