Open Access
2018 Tensor product of dualizing complexes over a field
Liran Shaul
J. Commut. Algebra 10(2): 243-263 (2018). DOI: 10.1216/JCA-2018-10-2-243


Let $\mathbb{k} $ be a field, and let $X$ and $Y$ be two locally noetherian $\mathbb{k} $-schemes (respectively, $\mathbb{k} $-formal schemes) with dualizing complexes $R_X$ and $R_Y$, respectively. We show that $R_X \boxtimes _{\mathbb{k} } R_Y$ (respectively, its derived completion) is a dualizing complex over $X\times _{\mathbb{k} } Y$ if and only if $X\times _{\mathbb{k} } Y$ is locally noetherian of finite Krull dimension.


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Liran Shaul. "Tensor product of dualizing complexes over a field." J. Commut. Algebra 10 (2) 243 - 263, 2018.


Published: 2018
First available in Project Euclid: 13 August 2018

zbMATH: 06917495
MathSciNet: MR3842336
Digital Object Identifier: 10.1216/JCA-2018-10-2-243

Primary: 13D09 , 13H10 , 13J10 , 18G20

Keywords: adic completion , dualizing complex

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

Vol.10 • No. 2 • 2018
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