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arXiv · 1809.04030

Polygones fondamentaux d'une courbe modulaire

Karim Belabas·Dominique Bernardi·Bernadette Perrin-Riou
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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 $SL_2(Z)$. 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 $Z[P^1(Q)]_0$.

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Karim Belabas, Dominique Bernardi, Bernadette Perrin-Riou. 2018-09-11. Polygones fondamentaux d'une courbe modulaire. https://arxiv.org/abs/1809.04030

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