The finite type of modules of bounded projective dimension and Serre's conditions

2023/11/24 by Hrbek, Michal, Gros, Giovanna Le · 1 citation
#13C05 #13C60 #13D07 #16E65 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2311.14346

Abstract

Let R be a commutative noetherian ring. We prove that the class of modules of projective dimension bounded by k is of finite type if and only if R satisfies Serre's condition (S_k). In particular, this answers positively a question of Bazzoni and Herbera in the specific setting of a Gorenstein ring. Applying similar techniques, we also show that the k-dimensional version of the Govorov-Lazard Theorem holds if and only if R satisfies the "almost" Serre condition (C_k+1).

Cited by

• Govorov--Lazard and finite deconstructibility for Gorenstein and restricted homological dimensions

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