Perfect complexes over an I-adic completion are equivalent to dualizable I-complete complexes precisely when the ring's Koszul homology is unchanged by completion.
Local dualisable objects in local algebra
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abstract
We discuss dualisable objects in minimal subcategories of compactly generated tensor triangulated categories, paying special attention to the derived category of a commutative noetherian ring. A cohomological criterion for detecting these local dualisable objects is established. Generalisations to other related contexts are discussed.
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Perfect complexes and completion
Perfect complexes over an I-adic completion are equivalent to dualizable I-complete complexes precisely when the ring's Koszul homology is unchanged by completion.