The Grothendieck theory of dessins d'enfants / edited by Leila Schneps.

Format:

Book

Contributor:

Schneps, Leila, editor.

Series:

London Mathematical Society lecture note series ; 200.

London Mathematical Society lecture note series ; 200

Language:

English

Subjects (All):

Dessins d'enfants (Mathematics).

Physical Description:

1 online resource (368 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1994.

Language Note:

English

Summary:

Dessins d'Enfants are combinatorial objects, namely drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action of the absolute Galois group on them. The study of this group via such realted combinatorial methods as its action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume. The various articles here unite all of the basics of the subject as well as the most recent advances. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.

Contents:

Noncongruence Subgroups, Covers and Drawings / B. Birch

Dessins d'enfants on the Riemann sphere / L. Schneps

Dessins from a geometric point of view / J.-M. Couveignes and L. Granboulan

Maps, Hypermaps and Triangle Groups / G. Jones and D. Singerman

Fields of definition of some three point ramified field extensions / G. Malle

On the classification of plane trees by their Galois orbit / G. Shabat

Triangulations / M. Bauer and C. Itzykson

Dessins d'enfant and Shimura varieties / P. Cohen

Horizontal divisors on arithmetic surfaces associated with Belyi uniformizations / Y. Ihara

Algebraic representation of the Teichmuller spaces / K. Saito

On the embedding of Gal[actual symbol not reproducible] into [actual symbol not reproducible] / Y. Ihara

Appendix: The action of the absolute Galois group on the moduli spaces of spheres with four marked points / M. Emsalem and P. Lochak.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-139-88508-1

1-107-36938-X

1-107-36458-2

1-107-36704-2

1-299-40474-X

1-107-36213-X

1-107-36953-3

1-107-37167-8

0-511-56930-0

OCLC:

843204382