Characterizing finite length local cohomology in terms of bounds on Koszul cohomology

JOURNAL OF ALGEBRA

卷:543

Article

Klein, Patricia¹ 

[1] Univ Minnesota, Dept Math, Minneapolis, MN 55455 USA

关键词: Koszul cohomology;    Local cohomology;    Hilbert-Samuel multiplicities;    Lech's inequality;   

DOI  :  10.1016/j.jalgebra.2019.09.026

来源: Elsevier

【 摘 要 】

Let (R, m, kappa) be a local ring. We give a characterization of R-modules M whose local cohomology is finite length up to some index in terms of asymptotic vanishing of Koszul cohomology on parameter ideals up to the same index. In particular, we show that a quasi-unmixed module M is asymptotically Cohen-Macaulay if and only if M is Cohen-Macaulay on the punctured spectrum if and only if sup{l(H-i(f(1), . . . ,f(d); M)) vertical bar root f(1), . . . ,f(d) = m, i < d} < infinity for d = dim(M) = dim(R). (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free