Perfect complexes and completion

Paul Balmer; Beren Sanders

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arXiv · 2411.14761

Perfect complexes and completion

Paul Balmer·Beren Sanders

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Abstract

Let $\hat{R}$ be the $I$-adic completion of a commutative ring $R$ with respect to a finitely generated ideal $I$. We give a necessary and sufficient criterion for the category of perfect complexes over $\hat{R}$ to be equivalent to the subcategory of dualizable objects in the derived category of $I$-complete complexes of $R$-modules. Our criterion is always satisfied when $R$ is noetherian. When specialized to $R$ local and noetherian and to $I$ the maximal ideal, our theorem recovers a recent result of Benson, Iyengar, Krause and Pevtsova.

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Paul Balmer, Beren Sanders. 2024-11-22. Perfect complexes and completion. https://arxiv.org/abs/2411.14761

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