ATTACHED PRIMES OF LOCAL COHOMOLOGY MODULES OF COMPLEXES

Let (R,𝔪) be a local ring, 𝒵 a specialization closed subset of Spec R and X an R-complex with finitely generated homology and finite dimension. We show that AttR H𝒵dim⁡X(X)={𝔭∈SuppR X∣cd(𝒵,R∕𝔭)−inf X𝔭=dimR X}. We also present a generalization of the Lichtenbaum–Hartshorne vanishing theorem for complexes of R-modules.