Some results on the annihilators and attached primes of local cohomology modules
Ali Atazadeh, Monireh Sedghi, Reza Naghipour

TL;DR
This paper investigates the structure of local cohomology modules over local rings, focusing on annihilators and attached primes, especially for relative Cohen-Macaulay modules and modules with specific cohomological properties.
Contribution
It provides new descriptions of annihilators and attached primes of local cohomology modules for relative Cohen-Macaulay modules and extends results to arbitrary modules over Noetherian rings.
Findings
Ann_R(H_{a}^{cd(a,M)}(M)) equals Ann_R M
Attached primes of H_{a}^{dim M - 1}(M) depend only on Supp(M)
For modules with cd(a,M)=cd(a,R/Ann_R M), attached primes are contained in primes with specific cohomological dimension
Abstract
Let be a local ring and a finitely generated -module. It is shown that if is relative Cohen-Macaulay with respect to an ideal of , then and where is the largest submodule of such that . We also show that if , then and so the attached primes of depends only on . Finally, we prove that if is an arbitrary module (not necessarily…
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