p-adic heights of generalized Heegner cycles

Ariel Shnidman

doi:10.5802/aif.3033

p-adic heights of generalized Heegner cycles

Ariel Shnidman^*

^*Corresponding author for this work

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

9 Scopus citations

Abstract

We relate the p-adic heights of generalized Heegner cycles to the derivative of a p-adic L-function attached to a pair (f, χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (ℓ, 0), with 0 < ℓ < 2r. This generalizes the p-adic Gross-Zagier formula in the case ℓ = 0 due to Perrin-Riou (in weight two) and Nekovář (in higher weight).

Original language	American English
Pages (from-to)	1117-1174
Number of pages	58
Journal	Annales de l'Institut Fourier
Volume	66
Issue number	3
DOIs	https://doi.org/10.5802/aif.3033
State	Published - 2016
Externally published	Yes

Bibliographical note

Funding Information:
I am grateful to Kartik Prasanna for suggesting this problem and for his patience and direction. Thanks go to Hunter Brooks for several productive conversations. I also thank Bhargav Bhatt, Daniel Disegni, Yara Elias, Olivier Fouquet, Adrian Iovita, Shinichi Kobayashi, Jan Nekovář, and Martin Olsson for helpful correspondence. The author was partially supported by National Science Foundation RTG grant DMS-0943832.

Publisher Copyright:
© 2016, Association des Annales de l'Institut Fourier. All rights reserved.

Keywords

Algebraic cycles
Modular forms
p-adic L-functions

Access to Document

10.5802/aif.3033

Cite this

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abstract = "We relate the p-adic heights of generalized Heegner cycles to the derivative of a p-adic L-function attached to a pair (f, χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (ℓ, 0), with 0 < ℓ < 2r. This generalizes the p-adic Gross-Zagier formula in the case ℓ = 0 due to Perrin-Riou (in weight two) and Nekov{\'a}{\v r} (in higher weight).",

keywords = "Algebraic cycles, Modular forms, p-adic L-functions",

author = "Ariel Shnidman",

note = "Funding Information: I am grateful to Kartik Prasanna for suggesting this problem and for his patience and direction. Thanks go to Hunter Brooks for several productive conversations. I also thank Bhargav Bhatt, Daniel Disegni, Yara Elias, Olivier Fouquet, Adrian Iovita, Shinichi Kobayashi, Jan Nekov{\'a}{\v r}, and Martin Olsson for helpful correspondence. The author was partially supported by National Science Foundation RTG grant DMS-0943832. Publisher Copyright: {\textcopyright} 2016, Association des Annales de l'Institut Fourier. All rights reserved.",

year = "2016",

doi = "10.5802/aif.3033",

language = "American English",

volume = "66",

pages = "1117--1174",

journal = "Annales de l'Institut Fourier",

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N2 - We relate the p-adic heights of generalized Heegner cycles to the derivative of a p-adic L-function attached to a pair (f, χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (ℓ, 0), with 0 < ℓ < 2r. This generalizes the p-adic Gross-Zagier formula in the case ℓ = 0 due to Perrin-Riou (in weight two) and Nekovář (in higher weight).

AB - We relate the p-adic heights of generalized Heegner cycles to the derivative of a p-adic L-function attached to a pair (f, χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (ℓ, 0), with 0 < ℓ < 2r. This generalizes the p-adic Gross-Zagier formula in the case ℓ = 0 due to Perrin-Riou (in weight two) and Nekovář (in higher weight).

KW - Algebraic cycles

KW - Modular forms

KW - p-adic L-functions

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JO - Annales de l'Institut Fourier

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ER -

p-adic heights of generalized Heegner cycles

Abstract

Bibliographical note

Keywords

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