Fundamental domains for Shimura curves

Kohel, David R., and Verrill, Helena A.. "Fundamental domains for Shimura curves." Journal de théorie des nombres de Bordeaux 15.1 (2003): 205-222. <http://eudml.org/doc/249088>.

@article{Kohel2003,
abstract = {We describe a process for defining and computing a fundamental domain in the upper half plane $\mathcal \{H\}^$ of a Shimura curve $X^D_0 (N)$ associated with an order in a quaternion algebra $A/ \mathbf \{Q\}$. A fundamental domain for $X^D_0 (N)$ realizes a finite presentation of the quaternion unit group, modulo units of its center. We give explicit examples of domains for the curves $X^6_0(1), \, X^\{15\}_0(1), \text\{ and \} X^\{35\}_0 (1)$. The first example is a classical example of a triangle group and the second is a corrected version of that appearing in the book of Vignéras [13], due to Michon. These examples are also treated in the thesis of Alsina [1]. The final example is new and provides a demonstration of methods to apply when the group action has no elliptic points.},
author = {Kohel, David R., Verrill, Helena A.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Shimura curves; fundamental domains; modular curves; quaternion algebras},
language = {eng},
number = {1},
pages = {205-222},
publisher = {Université Bordeaux I},
title = {Fundamental domains for Shimura curves},
url = {http://eudml.org/doc/249088},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Kohel, David R.
AU - Verrill, Helena A.
TI - Fundamental domains for Shimura curves
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 205
EP - 222
AB - We describe a process for defining and computing a fundamental domain in the upper half plane $\mathcal {H}^$ of a Shimura curve $X^D_0 (N)$ associated with an order in a quaternion algebra $A/ \mathbf {Q}$. A fundamental domain for $X^D_0 (N)$ realizes a finite presentation of the quaternion unit group, modulo units of its center. We give explicit examples of domains for the curves $X^6_0(1), \, X^{15}_0(1), \text{ and } X^{35}_0 (1)$. The first example is a classical example of a triangle group and the second is a corrected version of that appearing in the book of Vignéras [13], due to Michon. These examples are also treated in the thesis of Alsina [1]. The final example is new and provides a demonstration of methods to apply when the group action has no elliptic points.
LA - eng
KW - Shimura curves; fundamental domains; modular curves; quaternion algebras
UR - http://eudml.org/doc/249088
ER -