Title: Derived Complete Complexes at Weakly Proregular Ideals

Author: Amnon Yekutieli

Publication status: 

• Journal: Journal of Pure and Applied Algebra, Volume 229, Issue 3, March 2025. DOI https://doi.org/10.1016/j.jpaa.2025.107909

• Eprint: https://arxiv.org/abs/2309.01687 (2023) version 4 

Abstract: 

Weak proregularity of an ideal in a commutative ring is a subtle generalization of the noetherian property of the ring. Weak proregularity is of special importance for the study of derived completion, and it occurs quite often in non-noetherian rings arising in Hochschild and prismatic cohomologies.

This paper is about several related topics: adically flat modules, recognizing derived complete complexes, the structure of the category of derived complete complexes, and a derived complete Nakayama theorem - all with respect to a weakly proregular ideal; and the preservation of weak proregularity under completion of the ring. 

updated 27 Feb 2025