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• W2398756908 abstract "This work concerns the linearity defect of a module $M$ over a noetherian local ring $R$, introduced by Herzog and Iyengar in 2005, and denoted by $text{ld}_R M$. Roughly speaking, $text{ld}_R M$ is the homological degree beyond which the minimal free resolution of $M$ is linear. In the paper, it is proved that for any ideal $I$ in a regular local ring $R$ and for any finitely generated $R$-module $M$, each of the sequences $(text{ld}_R (I^nM))_n$ and $(text{ld}_R (M/I^nM))_n$ is eventually constant. The first statement follows from a more general result about the eventual constancy of the sequence $(text{ld}_R C_n)_n$ where $C$ is a finitely generated graded module over a standard graded algebra over $R$. The second statement follows from the first together with a result of Avramov on small homomorphisms." @default.
• W2398756908 created "2016-06-24" @default.
• W2398756908 creator A5025169288 @default.
• W2398756908 creator A5071238613 @default.
• W2398756908 date "2015-04-19" @default.
• W2398756908 modified "2023-09-27" @default.
• W2398756908 title "On the asymptotic behavior of the linearity defect" @default.
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