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Homological dimensions of complexes over coherent regular rings

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arxiv 2409.08393 v2 pith:USYMBPXR submitted 2024-09-12 math.AC

James Gillespie , Alina Iacob This is my paper · ORCID
classification math.AC
keywords coherentr-modulesdimensiondimensionsregularrespringsagrees
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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.

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