2004/12/09 by Srikanth B. Iyengar, Srikanth Iyengar, Tony J. Puthenpurakal +2
Mathematics · #13D07 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13D40 #Secondary 13D02 #math.AC #msc:13D02 #msc:13D07 #msc:13D40
paper · pdf · doi:10.48550/arxiv.math/0412194
revised version. To appear in Proc. Amer. Math. Soc
openalex publication_date 2004/12/09 · arxiv created 2005/07/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a finitely generated, non-free module M over a CM local ring (R,\fm,k), it is proved that for n≫ 0 the length of \tor 1RMR/\fmn+1 is given by a polynomial of degree dim R-1. The vanishing of \tor iRMN/\fmn+1N is studied, with a view towards answering the question: if there exists a finitely generated R-module N with dim N≥ 1 such that the projective dimension or the injective dimension of N/\fmn+1N is finite, then is R-regular? Upper bounds are provided for n beyond which the question has an affirmative answer.