UPPER BOUNDS FOR THE COHOMOLOGICAL DIMENSIONS OF FINITELY GENERATED MODULES OVER A COMMUTATIVE NOETHERIAN RING

被引：10

作者：

Ghasemi, Ghader ^{[1
]}

Bahmanpour, Kamal ^{[1
,2
]}

A'zami, Jafar ^{[1
]}

机构：

[1] Univ Mohaghegh Ardabili, Fac Math Sci, Dept Math, Ardebil 5619911367, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

来源：

COLLOQUIUM MATHEMATICUM | 2014年 / 137卷 / 02期

关键词：

cohomological dimension; local cohomology; Noetherian ring; system of parameters; ALGEBRAIC-VARIETIES; ARITHMETIC RANK; MATLIS DUALS; IDEAL;

D O I：

10.4064/cm137-2-10

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a commutative Noetherian ring, I a proper ideal of R, and M be a finitely generated R-module. We provide bounds for the cohomological dimension of the R-module M with respect to the ideal I in several cases.

引用

页码：263 / 270

页数：8

共 12 条

[1] Associated primes of local cohomology modules and Matlis duality [J].

Bahmanpour, Kamal ;

Naghipour, Reza .

JOURNAL OF ALGEBRA, 2008, 320 (06) :2632-2641

[2]

Brodmann M. P., 1998, LOCAL COHOMOLOGY ALG

[3] Cohomological dimension of certain algebraic varieties [J].

Divaani-Aazar, K ;

Naghipour, R ;

Tousi, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (12) :3537-3544

[4]

FALTINGS G, 1980, J REINE ANGEW MATH, V313, P43

[5]

Grothendieck A., 1967, Lect. Notes in Math., V41

[6] COHOMOLOGICAL DIMENSION OF ALGEBRAIC VARIETIES [J].

HARTSHORNE, R .

ANNALS OF MATHEMATICS, 1968, 88 (03) :403-+

[7]

Hellus M, 2008, P AM MATH SOC, V136, P489

[8] Matlis duals of top local cohomology modules and the arithmetic rank of an ideal [J].

Hellus, Michael .

COMMUNICATIONS IN ALGEBRA, 2007, 35 (04) :1421-1432

[9] ON THE VANISHING OF LOCAL COHOMOLOGY MODULES [J].

HUNEKE, C ;

LYUBEZNIK, G .

INVENTIONES MATHEMATICAE, 1990, 102 (01) :73-93

[10] On the finiteness of Bass numbers of local cohomology modules [J].

Kawasaki, K .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (11) :3275-3279

← 1 2 →