Arakelov Chow groups of abelian schemes, arithmetic Fourier transform, and analogues of the standard conjectures of Lefschetz type
type: Item
instance of: scholarly article
title: Arakelov Chow groups of abelian schemes, arithmetic Fourier transform, and analogues of the standard conjectures of Lefschetz type
zbMATH Open document ID: 0808.14020
DOI: 10.1007/BF01450492
author: Klaus Künnemann
published in: Mathematische Annalen
publication date: 1995-01-30T00:00:00Z
full work available at URL: https://eudml.org/doc/165258
review text: We discuss absolute and relative analogues of Grothendieck's standard conjectures of Lefschetz type for the arithmetic Chow groups introduced by Gillet and Soulé. We decompose the Arakelov Chow groups of an abelian scheme into eigenspaces with respect to \(n\)-multiplication and investigate their natural ring of correspondences. The main technical tool to obtain these results is an arithmetic analogue of the algebraic theory of the Fourier transform. We discuss filtrations on the arithmetic Chow groups and describe how the absolute hard Lefschetz conjecture of Gillet and Soulé can be derived from a relative version and a conjecture of Beilinson about the images of regulator maps in Deligne cohomology. Finally, we compute the cubical height of divisors on abelian schemes.
Mathematics Subject Classification ID: 14G40
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14C35
Mathematics Subject Classification ID: 14C17
Mathematics Subject Classification ID: 14K15
zbMATH DE Number: 701004
zbMATH Keywords: Beilinson conjecture
zbMATH Keywords: Grothendieck's standard conjectures of Lefschetz type
zbMATH Keywords: Arakelov Chow groups
zbMATH Keywords: filtrations on the arithmetic Chow groups
zbMATH Keywords: hard Lefschetz conjecture
zbMATH Keywords: regulator maps
zbMATH Keywords: cubical height of divisors
Wikidata QID: Q123344518
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 701004