Attached primes of local cohomology modules with respect to a pair of ideals

Abstract

The paper shows an extension of the Lichtenbaum–Hartshorne Vanishing theorem for local cohomology modules with respect to a pair of ideals. We also study the attached primes of top local cohomology module [Formula: see text] where [Formula: see text] In the case, where [Formula: see text] we show that [Formula: see text]

Local (Co)homology and Čech (Co)complexes with Respect to a Pair of Ideals

“…Subsequently, many authors have started studying local cohomology theory with respect to a pair of ideals. For example, Chu and Wang [19,20] investigated the top local cohomology module H dimM I,J (M) being Artinian, Payrovi and Parsa [21,22] showed the Artinianness and finiteness of local cohomology modules with respect to (I, J), and Nguyem [23] studied the attached primes of the top local cohomology module with respect to (I, J) in order to prove the Lichtenbaum-Hartshorne vanishing theorem for local cohomology modules with respect to (I, J). In 2015, Jorge Perez and Tobnon [24] introduced the (I, J)-completion submodule of M as Λ I,J (M) = lim ← − a∈ W(I,J) Λ a (M) = lim ← − a∈ W(I,J) lim ← − n∈N M/a n M, and considered local homology theory with respect to a pair of ideals.…”