Tensor product of dualizing complexes over a field

Abstract

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

13 pages, final version, to appear in the Journal of Commutative Algebra

References in corpus (1)

• Duality and Tilting for Commutative DG Rings

Cited by in corpus (2)

• Hochschild cohomology commutes with adic completion
• Completion and torsion over commutative DG rings