Intersection theory on algebraic stacks and on their moduli spaces
type: Item
instance of: scholarly article
title: Intersection theory on algebraic stacks and on their moduli spaces
zbMATH Open document ID: 0694.14001
DOI: 10.1007/BF01388892
author: Angelo Vistoli
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143716
review text: This article develops the theory of algebraic stacks due to Deligne and Artin, extending the notion of scheme, from ground level up to results: (1) Showing an algebraic stack having a moduli space admits a finite ramified covering by a scheme; (2) Characterizing those schemes of finite type over a field of characteristic 0 which are moduli spaces of some smooth stack; (3) Proving that Gysin homomorphisms for regular local embeddings of stacks pass to rational equivalence and commute among themselves; (4) Showing that the Chow group of a moduli space of an algebraic stack is isomorphic to the Chow group of the stack (despite the introduction). The moduli space of a smooth algebraic stack of finite type over a field is then shown to be an Alexander scheme (satisfying most of the formal intersection properties that smooth schemes do). Key inputs are intersection theory à la Fulton-MacPherson; Gillet's notion of a moduli space for an algebraic stack and Gillet's definition of Chow group for an algebraic stack of finite type of a field. The article is roughly speaking derived from the author's doctoral thesis.
Mathematics Subject Classification ID: 14C17
Mathematics Subject Classification ID: 18F20
Mathematics Subject Classification ID: 14F99
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14C35
zbMATH DE Number: 4136097
zbMATH Keywords: Gysin homomorphisms
zbMATH Keywords: Chow group
zbMATH Keywords: Alexander scheme
zbMATH Keywords: intersection theory
zbMATH Keywords: moduli space for an algebraic stack
zbMATH Keywords: Chow group for an algebraic stack
MaRDI profile type: Publication
cites work: Versal deformations and algebraic stacks
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description: scientific article; zbMATH DE number 4136097