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• W2964216409 abstract "Let R 0 be a Noetherian local ring and R a standard graded R 0 -algebra with maximal ideal 𝔪 and residue class field 𝕂 = R/𝔪. For a graded ideal I in R we show that for k ≫ 0: (1) the Artin-Rees number of the syzygy modules of I k as submodules of the free modules from a free resolution is constant, and thereby the Artin-Rees number can be presented as a proper replacement of regularity in the local situation; and (2) R is a polynomial ring over the regular R 0 , the ring R/I k is Golod, its Poincaré-Betti series is rational and the Betti numbers of the free resolution of 𝕂 over R/I k are polynomials in k of a specific degree. The first result is an extension of the work by Swanson on the regularity of I k for k ≫ 0 from the graded situation to the local situation. The polynomiality consequence of the second result is an analog of the work by Kodiyalam on the behaviour of Betti numbers of the minimal free resolution of R/I k over R." @default.
• W2964216409 created "2019-07-30" @default.
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• W2964216409 creator A5006798935 @default.
• W2964216409 creator A5080806048 @default.
• W2964216409 date "2016-09-26" @default.
• W2964216409 modified "2023-09-27" @default.
• W2964216409 title "Homology of Powers of Ideals: Artin-Rees Numbers of Syzygies and the Golod Property" @default.
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• W2964216409 doi "https://doi.org/10.1142/s1005386716000584" @default.
• W2964216409 hasPublicationYear "2016" @default.
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