An algebraic approach to the residues in algebraic geometry
type: Item
instance of: scholarly article
title: An algebraic approach to the residues in algebraic geometry
zbMATH Open document ID: 0664.13010
DOI: 10.1007/BF02570719
author: Zhongming Tang
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174110
review text: Let K/k be a finitely generated field of transcendence degree n and v a discrete valuation of rank n of \(K/k\). For any \(\omega\in \Omega^ n(K/k)\), we define the residue of \(\omega\) at v, \(Res_ v(\omega)\), as the sum of all the residues of \(\omega\) at the extensions of v in the inequivalent composites of K and \(\bar k\) over k. The paper shows that \(Res_ v\) is a well-defined k-map from \(\Omega^ n(K/k)\) to k and proves a theorem about the residues under a finite extension of the algebraic function field. Then, we define the residue of a differential form at a chain of points in a variety over an arbitrary field as the sum of the residues of the differential form at all the discrete valuations which have the chain of points as center.
Mathematics Subject Classification ID: 13N05
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 14F10
zbMATH DE Number: 4085788
zbMATH Keywords: algebraic function field
zbMATH Keywords: residue of a differential form
MaRDI profile type: Publication
cites work: Q5563439
cites work: Q5634095
cites work: Q4143433
cites work: Q3903085
cites work: Q3312356
cites work: Q3699804
cites work: Arithmetische Anwendungen der Differentialalgebren.
cites work: ON RESIDUES IN ALGEBRAIC GEOMETRY
cites work: Q3882554
cites work: Notes on differential theoretic characterization of regular local rings
cites work: ON THE ARITHMETIC OF TWO-DIMENSIONAL SCHEMES. I. DISTRIBUTIONS AND RESIDUES
cites work: Q3277020
cites work: Q5732721
description: scientific article; zbMATH DE number 4085788