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math.AC2023
An Ext-Tor duality theorem, cohomological dimension, and applications
Rafael Holanda, Cleto B. Miranda-Neto
We provide a duality theorem between Ext and Tor modules over a Cohen-Macaulay local ring possessing a canonical module, and use it to prove some freeness criteria for finite modul…
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…