Polygones fondamentaux d'une courbe modulaire
Number Theory
2019-10-07 v2
Abstract
A few pages in Siegel describe how, starting with a fundamental polygon for a compact Riemann surface, one can construct a symplectic basis of its homology. This note retells that construction, specializing to the case where the surface is associated to a congruence subgroup of . One then obtains by classical procedures a generating system for with a minimal number of hyperbolic elements and a presentation of the -module .
Cite
@article{arxiv.1809.04030,
title = {Polygones fondamentaux d'une courbe modulaire},
author = {Karim Belabas and Dominique Bernardi and Bernadette Perrin-Riou},
journal= {arXiv preprint arXiv:1809.04030},
year = {2019}
}
Comments
many figures, 33 pages, in french - A paraitre. Mathematiques de Besan\c{c}on : Algebre et Theorie des Nombres, Publications mathematiques de Besancon