, Volume 53, Issue 3, pp 573-592
Date: 31 Mar 2010

Arithmetic of Shimura curves

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This is the note for a series of lectures that the author gave at the Centre de Recerca Matemática (CRM), Bellaterra, Barcelona, Spain on October 19–24, 2009. The aim is to give a comprehensive description of some recent work of the author and his students on generalisations of the Gross-Zagier formula, Euler systems on Shimura curves, and rational points on elliptic curves.

Dedicated to Professor Yang Lo on the Occasion of his 70th Birthday