Some remarks on relative Tor and regular homomorphisms
type: Item
instance of: scholarly article
title: Some remarks on relative Tor and regular homomorphisms
zbMATH Open document ID: 1043.18006
author: Javier Majadas
published in: Rocky Mountain Journal of Mathematics
publication date: 2004-05-27T00:00:00Z
review text: The author proves a base change for relative \(\text{ Tor}\): given an \(S\)-module \(M\) and an \(S \otimes_R T\)-module \(N\), we have \(\text{ Tor}_n^{S \mid R}(M,N) = \text{ Tor}_n^{S \otimes_R T \mid T}(M \otimes_R T, N)\). Some application of this formula is given, e.g.\ for every homomorphism \(f: A \to B\) of Noetherian commutative rings, if \(\text{Tor}_n^{B \otimes_A B \mid B} (B,-)\) is zero for all \(n \geq m\) then the fibres of \(f\) are geometrically regular of dimension at most \(m\).
reviewed by: Gábor Braun
Mathematics Subject Classification ID: 18G25
Mathematics Subject Classification ID: 13B40
Mathematics Subject Classification ID: 13D05
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 16E30
zbMATH DE Number: 2067067
zbMATH Keywords: relative Tor
zbMATH Keywords: base change
zbMATH Keywords: geometrically regular fibers
zbMATH Keywords: flat homomorphism
zbMATH Keywords: Noetherian ring
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069945
OpenAlex ID: W1983950244
cites work: Q3240881
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DOI: 10.1216/RMJM/1181069945
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description: scientific article; zbMATH DE number 2067067