Heights of Heegner cycles and derivatives of L-series
type: Item
instance of: scholarly article
title: Heights of Heegner cycles and derivatives of L-series
zbMATH Open document ID: 0882.11029
published in: Inventiones Mathematicae
publication date: 1997-09-09T00:00:00Z
review text: The author extends Gross and Zagier's limit formula to high weight modular forms by using arithmetic intersection theory. More precisely, he defines the (global) height pairing between CM-cycles in certain Kuga-Sato varieties, and shows an identity between the height pairings of Heegner cycles and coefficients of certain cusp forms of high weights. He gives some applications to the generalized Birch and Swinnerton-Dyer conjecture of Beilinson and Bloch, and to the algebraicity conjecture of Gross and Zagier. He also shows that the index conjecture of Gillet-Soulé and Beilinson-Bloch, and the Generalized Riemann Hypothesis have a common consequence: the positivity of the derivatives of certain L-series.
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11G40
zbMATH DE Number: 1058848
zbMATH Keywords: Beilinson and Bloch conjecture
zbMATH Keywords: derivatives of L-series
zbMATH Keywords: limit formula
zbMATH Keywords: high weight modular forms
zbMATH Keywords: height pairings of Heegner cycles
zbMATH Keywords: algebraicity conjecture
zbMATH Keywords: index conjecture
zbMATH Keywords: Generalized Riemann Hypothesis
author: Shou-Wu Zhang
MaRDI profile type: Publication
full work available at URL: s002220050179
OpenAlex ID: W1985684082
DOI: 10.1007/S002220050179
description: scientific article; zbMATH DE number 1058848