Perfect complexes and completion

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.