Perfect complexes and completion
Commutative Algebra
2024-11-25 v1 Algebraic Topology
Category Theory
K-Theory and Homology
Abstract
Let be the -adic completion of a commutative ring with respect to a finitely generated ideal . We give a necessary and sufficient criterion for the category of perfect complexes over to be equivalent to the subcategory of dualizable objects in the derived category of -complete complexes of -modules. Our criterion is always satisfied when is noetherian. When specialized to local and noetherian and to the maximal ideal, our theorem recovers a recent result of Benson, Iyengar, Krause and Pevtsova.
Cite
@article{arxiv.2411.14761,
title = {Perfect complexes and completion},
author = {Paul Balmer and Beren Sanders},
journal= {arXiv preprint arXiv:2411.14761},
year = {2024}
}
Comments
20 pages