Some properties of top graded local cohomology modules
نویسندگان
چکیده
منابع مشابه
Some Properties of Top Graded Local Cohomology Modules
Let R = ⊕ d∈N0 Rd be a positively graded commutative Noetherian ring which is standard in the sense that R = R0[R1], and set R+ := ⊕ d∈N Rd, the irrelevant ideal of R. (Here, N0 and N denote the set of non-negative and positive integers respectively; Z will denote the set of all integers.) Let M = ⊕ d∈Z Md be a non-zero finitely generated graded R-module. This paper is concerned with the behavi...
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Let R be a commutative Noetherian ring, a an ideal of R, M and N be two finitely generated R-modules. Let t be a positive integer. We prove that if R is local with maximal ideal m and M ⊗R N is of finite length then H t m (M, N) is of finite length for all t ≥ 0 and lR(H t m (M, N)) ≤ ∑t i=0 lR(Ext i R (M, H m (N))). This yields, lR(H t m (M, N)) = lR(Ext t R(M, N)). Additionally, we show that ...
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All rings in this paper are commutative and Noetherian. If R is a ring and I ⊂ R is an ideal, cd(R, I) denotes the cohomological dimension of I in R, i.e. the largest integer i such that the i-th local cohomology module H i I(M) doesn’t vanish for some R-module M . For the purposes of this introduction R is a complete equicharacteristic regular local d-dimensional ring with a separably closed r...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2003
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00567-7