arXiv subjects

Bahmanpour

Publications and source records attributed to Bahmanpour.

3 recordsLinked to original sources

arXiv2019

A note on Abelian categories of cofinite modules

Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. In this article we answer affirmatively a question raised by the present author in \cite{B2}. Also, as an immediate consequence of this result it is shown that the category of all $I$-cofinite $R$-modules $\mathscr{C}(R, I)_{cof}$ is an Abelian subcategory of the category of all $R$-modules, whenever $q(I,R)\leq 1$. These assertions answer affirmatively a question raised by R. Hartshorne in [{\it Affine duality and cofiniteness}, Invent. Math. {\bf9}(1970), 145-164], in some special cases.

math.AC↗

arXiv2019

A study of cofiniteness through minimal associated primes

In this paper we shall investigate the concepts of cofiniteness of local cohomology modules and Abelian categories of cofinite modules over arbitrary Noetherian rings. Then we shall improve some of the results given in the literature.

math.AC↗

arXiv2019

Cofiniteness over Noetherian complete local rings

In this paper we prove the following generalization of a result of Hartshorne: Let $(S,\n)$ be a regular local ring of dimension $4$. Assume that $x,y,u,v$ is a regular system of parameters for $S$ and $a:=xu+yv$. Then for each finitely generated $S$-module $N$ with $\Supp N=V(aS)$ the socle of $H^2_{(u,v)S}(N)$ is infinite dimensional. Also, using this result, for any commutative Noetherian complete local ring $(R,\m)$, we characterize the class of all ideals $I$ of $R$ with the property that, for every finitely generated $R$-module $M$, the local cohomology modules $H^i_I(M)$ are $I$-cofinite for all $i\geq 0$.

math.AC↗