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

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

2 Scopus citations

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	English
Journal	Journal of the Institute of Mathematics of Jussieu
DOIs	https://doi.org/10.1017/S1474748021000608
State	Accepted/In press - 1 Jan 2022

Keywords

Heegner points
Keywords and phrases
p-adic L-functions
p-adic heights

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.1017/S1474748021000608

Cite this

@article{290af0ebc25b4051b9eed9a0e2b6fd9e,

title = "THE p-ADIC GROSS-ZAGIER FORMULA on SHIMURA CURVES, II: NONSPLIT PRIMES",

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.",

keywords = "Heegner points, Keywords and phrases, p-adic L-functions, p-adic heights",

author = "Daniel Disegni",

note = "Funding Information: I would like to thank the referees for a sharp reading. This research was supported by ISF grant 1963/20. Publisher Copyright: {\textcopyright} The Author(s), 2022. Published by Cambridge University Press.",

year = "2022",

month = jan,

day = "1",

doi = "10.1017/S1474748021000608",

language = "English",

journal = "Journal of the Institute of Mathematics of Jussieu",

issn = "1474-7480",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - THE p-ADIC GROSS-ZAGIER FORMULA on SHIMURA CURVES, II

T2 - NONSPLIT PRIMES

AU - Disegni, Daniel

N1 - Funding Information: I would like to thank the referees for a sharp reading. This research was supported by ISF grant 1963/20. Publisher Copyright: © The Author(s), 2022. Published by Cambridge University Press.

PY - 2022/1/1

Y1 - 2022/1/1

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.

KW - Heegner points

KW - Keywords and phrases

KW - p-adic L-functions

KW - p-adic heights

UR - http://www.scopus.com/inward/record.url?scp=85124961459&partnerID=8YFLogxK

U2 - 10.1017/S1474748021000608

DO - 10.1017/S1474748021000608

M3 - Article

AN - SCOPUS:85124961459

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

SN - 1474-7480

ER -

THE p-ADIC GROSS-ZAGIER FORMULA on SHIMURA CURVES, II: NONSPLIT PRIMES

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this