Academic Commons

Theses Doctoral

p-adic Heights of Heegner points on Shimura curves

Disegni, Daniel

Let f be a primitive Hilbert modular form of weight 2 and level N for the totally real field F, and let p be an odd rational prime such that f is ordinary at all primes dividing p. When E is a CM extension of F of relative discriminant prime to Np, we give an explicit construction of the p-adic Rankin-Selberg L-function L_p(f_E,-) and prove that when the sign of its functional equation is -1, its central derivative is given by the p-adic height of a Heegner point on the abelian variety A associated to f. This p-adic Gross-Zagier formula generalises the result obtained by Perrin-Riou when F=Q and N satisfies the so-called Heegner condition. We deduce applications to both the p-adic and the classical Birch and Swinnerton-Dyer conjectures for A.



  • thumnail for Disegni_columbia_0054D_11281.pdf Disegni_columbia_0054D_11281.pdf binary/octet-stream 522 KB Download File

More About This Work

Academic Units
Thesis Advisors
Zhang, Shou-Wu
Ph.D., Columbia University
Published Here
May 1, 2013
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.