2024/11/22 by Paul Balmer, Beren Sanders, Balmer, Paul +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2411.14761
Let 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 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.