Asymptotic behavior of homological invariants of localizations of modules

2023/10/18 by Kimura, Kaito
#13A30 #13D05 #13D07 #13D40 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2310.11697

Abstract

Let R be a commutative noetherian ring, I an ideal of R, and M a finitely generated R-module. We consider the asymptotic injective dimensions, projective dimensions, Bass numbers, and Betti numbers of localizations of M/Iⁿ M at prime ideals of R and prove that these invariants are stable or have polynomial growth for large integers n that do not depend on the prime ideals.

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