Homological dimensions of complexes over coherent regular rings

TL;DR

This paper extends homological dimension characterizations of regularity from Noetherian to coherent rings, showing equivalences involving injective, projective, FP-injective, and flat dimensions of complexes.

Contribution

It generalizes Iacob-Iyengar's results to coherent rings, broadening the understanding of homological dimensions in non-Noetherian contexts.

Findings

Equivalence of regularity and dimension conditions for complexes over coherent rings

Extension of Iacob-Iyengar's results from Noetherian to coherent rings

Homological dimensions based on FP-injective and flat modules also characterize regularity

Abstract

We show that Iacob-Iyengar's answer to a question of Avromov-Foxby extends from Noetherian to coherent rings. In particular, a coherent ring R is regular if and only if the injective (resp. projective) dimension of each complex X of R-modules agrees with its graded-injective (resp. graded-projective) dimension. The same is shown for the analogous dimensions based on FP-injective R-modules, and on flat R-modules.