padic Heights of Heegner points on Shimura curves
 Title:
 padic Heights of Heegner points on Shimura curves
 Author(s):
 Disegni, Daniel
 Thesis Advisor(s):
 Zhang, ShouWu
 Date:
 2013
 Type:
 Dissertations
 Department(s):
 Mathematics
 Persistent URL:
 http://hdl.handle.net/10022/AC:P:20097
 Notes:
 Ph.D., Columbia University.
 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 padic RankinSelberg Lfunction L_p(f_E,) and prove that when the sign of its functional equation is 1, its central derivative is given by the padic height of a Heegner point on the abelian variety A associated to f. This padic GrossZagier formula generalises the result obtained by PerrinRiou when F=Q and N satisfies the socalled Heegner condition. We deduce applications to both the padic and the classical Birch and SwinnertonDyer conjectures for A.
 Subject(s):
 Mathematics
 Item views
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 Suggested Citation:
 Daniel Disegni, 2013, padic Heights of Heegner points on Shimura curves, Columbia University Academic Commons, http://hdl.handle.net/10022/AC:P:20097.