Arithmetic of quaternion algebras and Shimura curves

02/13/2018 - 12:15pm
02/13/2018 - 1:10pm
Laia Amoros (Aalto University, Finland)

I will introduce quaternion algebras and show how one can construct Shimura curves with them. Quaternion algebras arise as a natural generalisation of matrix algebras. In the same way that the action of SL(2,Q) (and of all its congruence subgroups) on the complex upper half-plane give us modular curves, the action of certain subgroups of quaternion algebras will give us some algebraic structure (the so called Shimura curves). After this introduction I will explain some applications of Shimura curves and sketch how one can compute the bad reduction of certain families of Shimura curves, based on a joint work with P. Milione.

Millikan 2099, Pomona College

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