Abstract
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.
Citation
Liran Shaul. "Tensor product of dualizing complexes over a field." J. Commut. Algebra 10 (2) 243 - 263, 2018. https://doi.org/10.1216/JCA-2018-10-2-243
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