Home /  NGM Pizza Seminar: The p-adic Gross-Zagier formula on Shimura curves.


NGM Pizza Seminar: The p-adic Gross-Zagier formula on Shimura curves. September 12, 2014 (11:00 AM PDT - 11:45 AM PDT)
Parent Program:
Location: SLMath: Eisenbud Auditorium
Speaker(s) Daniel Disegni (Ben Gurion University of the Negev)
Description No Description
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
No Video Uploaded

For elliptic curves E/Q whose L-function L=L(E,s) vanishes to order one at s=1, the rank of E(Q) is also known to be one. This is the first prediction of the Birch and Swinnerton-Dyer conjecture, and the main ingredient of the proof is the formula of Gross and Zagier relating the heights of modularly-constructed points on E to the central derivative of L. The second prediction of BSD is a formula for the central leading term of L. This is only implied by the Gross-Zagier formula up to a nonzero rational number. One way to go on and study the BSD formula up to p-integrality is provided by a p-adic analogue of the Gross-Zagier formula due to Perrin-Riou and Kobayashi. I will explain this circle of ideas as well as its generalization to totally real fields. Time permitting, I will also discuss the representation-theoretic context.


The talk is meant to be accessible to a broad audience.

No Notes/Supplements Uploaded No Video Files Uploaded