Arakelov Chow groups of abelian schemes, arithmetic Fourier transform, and analogues of the standard conjectures of Lefschetz type

DOI10.1007/BF01450492zbMath0808.14020WikidataQ123344518 ScholiaQ123344518MaRDI QIDQ1340163

Klaus Künnemann

Publication date: 30 January 1995

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165258

zbMATH Keywords

Beilinson conjectureregulator mapsArakelov Chow groupscubical height of divisorsfiltrations on the arithmetic Chow groupsGrothendieck's standard conjectures of Lefschetz typehard Lefschetz conjecture

Mathematics Subject Classification ID

Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Parametrization (Chow and Hilbert schemes) (14C05) Arithmetic ground fields for abelian varieties (14K15) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35)

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Minimal heights and polarizations on group varieties ⋮ The Maillot-Rössler current and the polylogarithm on abelian schemes ⋮ Chow motives of abelian type over a base ⋮ Weil-étale cohomology and zeta-values of proper regular arithmetic schemes ⋮ Unnamed Item ⋮ Higher arithmetic \(K\)-theory

Cites Work

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• Groupes de Chow et K-théorie de variétés sur un corps fini
• Higher regulators and values of \(L\)-functions
• Arithmetic intersection theory
• Green's currents and height pairing on complex tori
• On a conjectural filtration on the Chow groups of an algebraic variety. I: The general conjectures and some examples
• A Lefschetz decomposition for Chow motives of abelian schemes
• Positive line bundles on arithmetic surfaces
• An arithmetic Riemann-Roch theorem
• Faisceaux amples sur les schémas en groupes et les espaces homogènes
• Duality between D(X) and with its application to picard sheaves