Abstract
Given a commutative ring R and finitely generated ideal I, one can consider the classes of I-adically complete, L-0(I)-complete and derived I -complete complexes. Under a mild assumption on the ideal I called weak pro-regularity, these three notions of completions interact well.
We consider the classes of I-adically complete, L-0(I)-complete and derived I -complete complexes and prove that they present the same homotopy theory. Given a ring homomorphism R ->& nbsp; S, we then give necessary and sufficient conditions for the categories of complete R complexes and the categories of complete S -complexes to have equivalent homotopy theories.
This recovers and generalizes a result of Sather-Wagstaff and Wicklein on extended local (co)homology. (C)& nbsp;2021 Elsevier Inc. All rights reserved.