Published on *Max-Planck-Institut für Mathematik* (http://www.mpim-bonn.mpg.de)

Posted in

- Vortrag [1]

Speaker:

Jeroen Sijsling
Zugehörigkeit:

Utrecht U/MPI
Datum:

Mit, 09/02/2011 - 14:15 - 15:15 A (1;e)-curve is a quotient of the upper half plane that is of genus 1 and ramifies above only one point. We explore the finite list, due to Kisao Takeuchi, of arithmetic (1;e)-curves, which are those (1;e)-curves that allow a natural finite-to-one correspondence with a Shimura curve coming from a quaternion algebra over a totally real field. After defining the notion of a canonical model of such an arithmetic (1;e)-curve, we show how to calculate these canonical models by using explicit methods such as p-adic uniformizations and Belyi maps along with modular techniques involving the Shimura congruence relation and Hilbert modular forms.

**Links:**

[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/de/node/3444

[3] http://www.mpim-bonn.mpg.de/de/node/246