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p-adic Heights of Heegner points on Shimura curves

Daniel Disegni

Title:
p-adic Heights of Heegner points on Shimura curves
Author(s):
Disegni, Daniel
Thesis Advisor(s):
Zhang, Shou-Wu
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
Abstract:
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.
Subject(s):
Mathematics
Item views
758
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Suggested Citation:
Daniel Disegni, , p-adic Heights of Heegner points on Shimura curves, Columbia University Academic Commons, .

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