Polygones fondamentaux d'une courbe modulaire

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 $\Gamma$ of $S{L}_2(Z)$. One then obtains by classical procedures a generating system for $\Gamma$ with a minimal number of hyperbolic elements and a presentation of the $Z[\Gamma ]$-module $Z[P^1(Q){]}_0$.

many figures, 33 pages, in french - A paraitre. Mathematiques de Besançon : Algebre et Theorie des Nombres, Publications mathematiques de Besancon