English

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 Γ\Gamma of SL2(Z)SL_2(Z). One then obtains by classical procedures a generating system for Γ\Gamma with a minimal number of hyperbolic elements and a presentation of the Z[Γ]Z[\Gamma]-module Z[P1(Q)]0Z[P^1(Q)]_0.

Keywords

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

R2 v1 2026-06-23T04:02:45.576Z