Weakly cofiniteness of local cohomology modules

2017/07/21 by Aghapournahr, Moharram
#13D45 #13E05 #14B15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.06795

Abstract

Let R be a commutative Noetherian ring, Φ a system of ideals of R and I∈ Φ. Let M be an R-module (not necessary I-torsion) such that dim M≤ 1, then the R-module \Extⁱ_R(R/I, M) is weakly Laskerian, for all i≥ 0, if and only if the R-module \Extⁱ_R(R/I, M) is weakly Laskerian, for i=0, 1. Let t∈ℕ₀ be an integer and M an R-module such that \Extⁱ_R(R/I,M) is weakly Laskerian for all i≤ t+1. We prove that if the R-module \lcⁱ_Φ(M) is \rm FD_{≤ 1} for all i

Related

• Cofiniteness of local cohomology modules for ideals of dimension one
• Hartshorne's questions and weakly cofiniteness
• Cofiniteness of weakly Laskerian local cohomology modules
• Modules cofinite and weakly cofinite with respect to an ideal
• Associated primes of local cohomology modules of weakly Laskerian\n modules