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

Seminar

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: New Geometric Methods in Number Theory and Automorphic Forms
Location: MSRI: Simons Auditorium
Speaker(s) Daniel Disegni (McGill University)
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Abstract/Media

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.

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