The P-Adic Gross-Zagier Formula on Shimura Curves, Ii: Nonsplit Primes

Daniel Disegni

doi:10.1017/S1474748021000608

The P-Adic Gross-Zagier Formula on Shimura Curves, Ii: Nonsplit Primes

Daniel Disegni

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

The formula of the title relates p-adic heights of Heegner points and derivatives of p-adic L-functions. It was originally proved by Perrin-Riou for p-ordinary elliptic curves over the rationals, under the assumption that p splits in the relevant quadratic extension. We remove this assumption, in the more general setting of Hilbert-modular abelian varieties.

Original language	American English
Pages (from-to)	2199-2240
Number of pages	42
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	22
Issue number	5
DOIs	https://doi.org/10.1017/S1474748021000608
State	Published - 15 Sep 2023

Keywords

Heegner points
p-adic L-functions
p-adic heights

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/S1474748021000608

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abstract = "The formula of the title relates p-adic heights of Heegner points and derivatives of p-adic L-functions. It was originally proved by Perrin-Riou for p-ordinary elliptic curves over the rationals, under the assumption that p splits in the relevant quadratic extension. We remove this assumption, in the more general setting of Hilbert-modular abelian varieties.",

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N2 - The formula of the title relates p-adic heights of Heegner points and derivatives of p-adic L-functions. It was originally proved by Perrin-Riou for p-ordinary elliptic curves over the rationals, under the assumption that p splits in the relevant quadratic extension. We remove this assumption, in the more general setting of Hilbert-modular abelian varieties.

AB - The formula of the title relates p-adic heights of Heegner points and derivatives of p-adic L-functions. It was originally proved by Perrin-Riou for p-ordinary elliptic curves over the rationals, under the assumption that p splits in the relevant quadratic extension. We remove this assumption, in the more general setting of Hilbert-modular abelian varieties.

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The P-Adic Gross-Zagier Formula on Shimura Curves, Ii: Nonsplit Primes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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