Kamal Bahmanpour

Cofiniteness of Local Cohomology Modules

Let M be a non-zero finitely generated module over a commutative Noetherian local ring (R, 𝔪). In this paper we consider when the local cohomology modules are finitely generated. It is shown that if t ≥ 0 is an integer and

On the category of cofinite modules which is Abelian

\mathfrak{p}\in {\rm Supp\,} H^{t}_\mathfrak{p}(M)

ARITHMETIC RANK, COHOMOLOGICAL DIMENSION AND FILTER REGULAR SEQUENCES

, then

A Note on the Artinian Cofinite Modules

H^{t+\dim R/\mathfrak{p}}_\mathfrak{m}(M)

FINITENESS PROPERTIES OF EXTENSION FUNCTORS OF COFINITE MODULES

is not 𝔭-cofinite. Then we obtain a partial answer to a question raised by Huneke. Namely, if R is a complete local ring, then

Modules cofinite and weakly cofinite with respect to an ideal

H^{n}_\mathfrak{m}(M)

A note on Lynch’s conjecture

is finitely generated if and only if 0 ≤ n ∉ W, where

On the cofiniteness of Artinian local cohomology modules

W=\{t+\dim R/\mathfrak{p}\,|\,\mathfrak{p}\in {\rm Supp\,} H^t_\mathfrak{p}(M)\backslash V(\mathfrak{m})\}

A Note on Cofinite Modules

. Also, we show that if J ⊆ I are 1-dimensional ideals of R, then

ON THE FINITENESS OF BASS NUMBERS OF LOCAL COHOMOLOGY MODULES

H^t_I(M)