The associated primes of local cohomology modules over rings of small dimension
The associated primes of local cohomology modules over rings of small dimension
复制标题
小维环上局部上同调模的相关素数
DOI：
10.1007/s002290170024
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发表时间：
2001
影响因子：
0.6
通讯作者：
T. Marley
中科院分区：
文献类型：
--
作者：
T. Marley
设R是第二维交换Noether局部环，R的Ian理想，Ma_n生成R-模。本文证明了局部上同调模HiI（M）的伴随素数集在下列情形下对所有i ≥ 0是有限的：（1）d≤ 3;（2）d= 4，且在删余谱上是正则的;（3）d= 5，R是非分歧正则局部环，且M是无挠的.另外，如果Hd − 1 I（M）对任意R，I和M都有有限支集。
LetRbe a commutative Noetherian local ring of dimensiond,Ian ideal ofR, andMa finitely generatedR-module. We prove that the set of associated primes of the local cohomology moduleHiI(M) is finite for alli≥ 0 in the following cases: (1)d≤ 3; (2)d= 4 andis regular on the punctured spectrum; (3)d= 5,Ris an unramified regular local ring, andMis torsion-free. In addition, ifthenHd− 1I(M) has finite support for arbitraryR,I, andM.