THE<i>p</i>-ADIC GROSS–ZAGIER FORMULA ON SHIMURA CURVES, II: NONSPLIT PRIMES-Reference-Cited by-同舟云学术

THEp-ADIC GROSS–ZAGIER FORMULA ON SHIMURA CURVES, II: NONSPLIT PRIMES

Published:2022-02-15 Issue: Volume: Page:1-42
ISSN:1474-7480
Container-title:Journal of the Institute of Mathematics of Jussieu
language:en
Short-container-title:J. Inst. Math. Jussieu

Author:

Disegni Daniel^ORCID

Abstract

AbstractThe formula of the title relatesp-adic heights of Heegner points and derivatives ofp-adicL-functions. It was originally proved by Perrin-Riou forp-ordinary elliptic curves over the rationals, under the assumption thatpsplits in the relevant quadratic extension. We remove this assumption, in the more general setting of Hilbert-modular abelian varieties.

Funder

Israel Science Foundation

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference29 articles.

1. Motivic p-adic L-functions

2. [4] Büyükboduk, K. , Pollack, R. and Sasaki, S. , ‘p-adic Gross-Zagier formula at critical slope and a conjecture of Perrin-Riou, Preprint, 2021, https://arxiv.org/pdf/1811.08216.pdf.

3. Selmer Complexes;Nekovář;Astérisque,2006

4. Sur la mauvaise réduction des courbes de Shimura;Carayol;Compos. Math.,1986

5. Onp-adic analogues of the conjectures of Birch and Swinnerton-Dyer

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. $p$-adic equidistribution of CM points;Commentarii Mathematici Helvetici;2022-12-14

2. The universal p-adic Gross–Zagier formula;Inventiones mathematicae;2022-07-25

3. p-adic L-functions via local–global interpolation: the case of;Canadian Journal of Mathematics;2022-06-13