Linear forms, algebraic cycles, and derivatives of \(L\)-series
type: Item
instance of: scholarly article
title: Linear forms, algebraic cycles, and derivatives of \(L\)-series
zbMATH Open document ID: 1443.11077
published in: Science China. Mathematics
publication date: 2019-11-27T00:00:00Z
review text: In this paper, the author states some refinements of conjectures due to Gan-Gross-Prasad and Kudla, relating central derivatives of automorphic \(L\)-functions to height pairings of special cycles on Shimura varieties. He also considers analogous conjectures for central values where height pairings are replaced by certain invariant linear forms on spaces of automorphic representations. With the inclusion of many references, this short survey article may serve as an overview on recent progress within the very influential circle of ideas relating special values of automorphic \(L\)-functions to the arithmetic geometry of Shimura varieties.
reviewed by: Nils Matthes
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11J20
Mathematics Subject Classification ID: 14C25
zbMATH DE Number: 7137540
zbMATH Keywords: linear forms
zbMATH Keywords: algebraic cycles
zbMATH Keywords: derivatives
zbMATH Keywords: \(L\)-series
author: Shou-Wu Zhang
MaRDI profile type: Publication
full work available at URL: s11425-019-1589-7
OpenAlex ID: W2184678485
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DOI: 10.1007/S11425-019-1589-7
description: scientific article; zbMATH DE number 7137540