Perfect complexes and completion

Abstract

Let

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

R ^ ${\hat {R}}_{}$ ModifyingAbove upper R With caret

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.