ABC for polynomials, dessins d'enfants, and uniformization : a survey

  • The main subject of this survey are Belyi functions and dessins d'enfants on Riemann surfaces. Dessins are certain bipartite graphs on 2-mainfolds defining there are conformal and even an algebraic structure. In principle, all deeper properties of the resulting Riemann surfaces or algebraic curves should be encoded in these dessins, but the decoding turns out to be difficult and leads to many open problems. We emphasize arithmetical aspects like Galois actions, the relation to the ABC theorem in function filds and arithemtic questions in uniformization theory of algebraic curves defined over number fields.

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Author:Jürgen WolfartGND
Parent Title (German):Elementare und analytische Zahlentheorie : (Tagungsband) ; proceedings ELAZ-conference May 24-28, 2004
Place of publication:Stuttgart
Document Type:Conference Proceeding
Date of Publication (online):2005/06/27
Year of first Publication:2005
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/06/27
Page Number:36
First Page:313
Last Page:345
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht