Cofiniteness of Local Cohomology Modules

• 作者: Kamal Bahmanpour Monireh Sedghi Reza Naghipour
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 生成模块 上同调 有限生成 极大极小 局部环 滤波器 IM 非零
• 年，卷（期）: 2014,（4）
• 页码范围: 605-614
• 页数: 10页
• 分类号: O152.5
• 语种: 中文

摘要

Let M be a non-zero finitely generated module over a commutative Noetherian local ring (R, m). In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t≥ 0 is an integer and p C Supp H^t_p (M), then Hm^t+dim R/p (M) is not p-cofinite. Then we obtain a partial answer to a question raised by Huneke. Namely, if R is a complete local ring, then H^n_m (M) is finitely generated if and only if 0 ≤ n ￠ W, where W ---- {t + dimR/p丨p ∈ SuppH^t_p(M)/V(m)}. Also, we show that if J C I are 1-dimensional ideals of R, then H^t_I(M) is J-cominimax, and H^t_I(M) is finitely generated (resp., minimax) if and only if H}R, (Mp) is finitely generated for all p C Spec R (resp., p ∈ SpecR/MaxR). Moreover, the concept of the J-cofiniteness dimension cJ(M) of M relative to I is introduced, and we explore an interrelation between c^I_m(M) and the filter depth of M in I. Finally, we show that if R is complete and dim M/IM ≠ 0, then c^I_m (R) ---- inf{depth Mp + dim R/p 丨 P ∈ Supp M/IM/V(m)}.