##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Francesc Castella

#### UCLA

## Lambda-adic Gross-Zagier formula for supersingular primes

##### Abstract:

In 2013, Kobayashi proved an analogue of Perrin-Riou's p-adic Gross-Zagier formula for supersingular primes. In this talk, we will explain an extension of Kobayashi's result to the Lambda-adic setting. The main formula is in terms of plus/minus Heegner points up the anticyclotomic tower, and its proof, rather than on calculations inspired by the original work of Gross-Zagier, is via Iwasawa theory, based on the connection between Heegner points, Beilinson-Flach elements, and different p-adic L-functions. (Joint work in progress with Xin Wan.)

Host: Claus Sorensen

### May 5, 2016

### 2:00 PM

### AP&M 7321

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