Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Balmer, Paul, Sanders, Beren
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4404985934