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math.AC2024
Cohen-Macaulay pairs
Rafael Holanda, Cleto B. Miranda-Neto
The main purpose of this note is to extend and establish a new approach to the concept of (relative) Cohen-Macaulayness, by investigating the cohomological dimension as well as the…
math.AC2023
Homology of multiple complexes and Mayer-Vietoris spectral sequences
Marc Chardin, Rafael Holanda, José Naéliton
Similarities are noted in two Mayer-Vietoris spectral sequences that generalize to any number of ideals in the Mayer-Vietoris exact sequence in local cohomology for two ideals. One…
math.AC2023
Generalized Hartshorne's problem on finiteness properties of local cohomology modules
André Dosea, Rafael Holanda, Cleto B. Miranda-Neto
Our main goal in this paper is to answer new positive cases of the natural generalized version of Hartshorne's celebrated question on cofiniteness of local cohomology modules, and…