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June 2015 The $\ast$-transforms of Acyclic Complexes
Taro INAGAWA
Tokyo J. Math. 38(1): 211-225 (June 2015). DOI: 10.3836/tjm/1437506245

Abstract

Let $R$ be an $n$-dimensional Cohen-Macaulay local ring and $Q$ a parameter ideal of $R$. Suppose that an acyclic complex $(F_{\bullet}, \varphi_{\bullet})$ of length $n$ of finitely generated free $R$-modules is given. We put $M = {\rm Im} \, \varphi_{1}$, which is an $R$-submodule of $F_{0}$. Then $F_{\bullet}$ is an $R$-free resolution of $F_{0}/M$. In this paper, we describe a concrete procedure to get an acyclic complex $^\ast\!{F_{\bullet}}$ of length $n$ that resolves $F_{0}/(M :_{F_{0}} Q)$.

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Taro INAGAWA. "The $\ast$-transforms of Acyclic Complexes." Tokyo J. Math. 38 (1) 211 - 225, June 2015. https://doi.org/10.3836/tjm/1437506245

Information

Published: June 2015
First available in Project Euclid: 21 July 2015

zbMATH: 1328.13018
MathSciNet: MR3374622
Digital Object Identifier: 10.3836/tjm/1437506245

Rights: Copyright © 2015 Publication Committee for the Tokyo Journal of Mathematics

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Vol.38 • No. 1 • June 2015
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