English

Perfect complexes and completion

Commutative Algebra 2024-11-25 v1 Algebraic Topology Category Theory K-Theory and Homology

Abstract

Let R^\hat{R} be the II-adic completion of a commutative ring RR with respect to a finitely generated ideal II. We give a necessary and sufficient criterion for the category of perfect complexes over R^\hat{R} to be equivalent to the subcategory of dualizable objects in the derived category of II-complete complexes of RR-modules. Our criterion is always satisfied when RR is noetherian. When specialized to RR local and noetherian and to II the maximal ideal, our theorem recovers a recent result of Benson, Iyengar, Krause and Pevtsova.

Keywords

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

R2 v1 2026-06-28T20:08:44.583Z