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Canonical models of arithmetic (1;e)-curves

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Jeroen Sijsling
Utrecht U/MPI
Wed, 09/02/2011 - 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

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.

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