2023/09/04 by Yekutieli, Amnon
#13D09 #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.2309.01687
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.