Arithmetic intersection theory
type: Item
instance of: scholarly article
title: Arithmetic intersection theory
zbMATH Open document ID: 0741.14012
DOI: 10.1007/BF02699132
published in: Publications Mathématiques
publication date: 1992-06-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104073
review text: The article constructs an intersection-product on the arithmetic Chow groups \(\widehat{Ch}\) of regular schemes over the integers of number- fields. These groups are quotients of pairs \((Z,g_ Z)\), \(Z\) a cycle and \(g_ Z\) a ``Green's current'', under rational equivalence. The main two difficulties are first to define the product of Green's currents (which needs some regularity-considerations) and second an analytic version of Chow's moving lemma. It should be noted that, as in the purely algebraic case, the theory becomes much simpler if one only attempts to intersect with Chern-classes of hermitian bundles (these have been defined earlier by the same authors).
Mathematics Subject Classification ID: 14G40
Mathematics Subject Classification ID: 14C25
zbMATH DE Number: 7231
zbMATH Keywords: intersection-product on the arithmetic Chow groups
zbMATH Keywords: Green's currents
zbMATH Keywords: Chow's moving lemma
author: Henri Gillet
author: Christophe Soulé
MaRDI profile type: Publication
Wikidata QID: Q58947683
cites work: INTERSECTION THEORY OF DIVISORS ON AN ARITHMETIC SURFACE
cites work: Q4120664
cites work: Riemann-Roch for singular varieties
cites work: Higher regulators and values of \(L\)-functions
cites work: Q3795767
cites work: Height pairings for algebraic cycles
cites work: Algebraic K-theory and classfield theory for arithmetic surfaces
cites work: Algebraic cycles and higher K-theory
cites work: Q3972723
cites work: La classe d'homologie fondamentale d'un espace analytique
cites work: Homology theory for locally compact spaces
cites work: Q4772354
cites work: Analytic cycles and vector bundles on non-compact algebraic varieties
cites work: Formes différentielles et cohomologie sur une variété analytique complexe
cites work: Q5813687
cites work: Calculus on arithmetic surfaces
cites work: Q3328651
cites work: Riemann-Roch theorems for higher algebraic K-theory
cites work: Some New Gysin Homomorphisms for the Chow Homology of Varieties
cites work: Q3758019
cites work: K-theory and intersection theory revisited
cites work: Q3745948
cites work: Q3754089
cites work: Intersection theory using Adams operations
cites work: Characteristic classes for algebraic vector bundles with Hermitian metric. I
cites work: The K-theory of hereditary categories
cites work: Localization for flat modules in algebraic K-theory
cites work: Q4195061
cites work: Q4084975
cites work: Duality and the de Rham cohomology of infinitesimal neighborhoods
cites work: Resolution of singularities of an algebraic variety over a field of characteristic zero. I
cites work: Heights and Arakelov's Intersection Theory
cites work: Q3729305
cites work: The currents defined by analytic varieties
cites work: Global Residues and Intersections on a Complex Manifold
cites work: The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
cites work: Q5612629
cites work: Intégration sur un ensemble analytique complexe
cites work: Higher algebraic K-theory: I
cites work: Q5528072
cites work: Q3677990
cites work: Opérations En K-Théorie Algébrique
cites work: Q5522742
cites work: Q3912492
cites work: Q5677789
reviewed by: Gerd Faltings
description: scientific article; zbMATH DE number 7231