11 papers
Finite projective dimension and a question of Jorgensen
Rafael Holanda, Cleto B. Miranda-Neto
This paper studies finite projective dimension of finitely generated modules over a Noetherian local ring, by means of spectral sequence methods related to generalized local cohomo…
Multiple Tor modules: rigidity and Mayer-Vietoris spectral sequences
Arindam Banerjee, Marc Chardin, Rafael Holanda
We extend some properties of a pair of ideals described in terms of Tor modules to any number of ideals, including the well-known rigidity property. Those extensions require the de…
On Extension modules of finite homological dimension
Rafael Holanda, Victor H. Jorge-Pérez, Victor D. Mendoza-Rubio
We explore the implications of the finiteness of homological dimensions for Ext modules, focusing on projective dimension, injective dimension, and their Gorenstein counterpart. In…
Homological dimensions, the Gorenstein property, and special cases of some conjectures
Souvik Dey, Rafael Holanda, Cleto B. Miranda-Neto
Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the projective and injective dimensions of a finite module over a (commutative)…
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…
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…
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…
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…
Vanishing of (co)homology, freeness criteria, and the Auslander-Reiten conjecture for Cohen-Macaulay Burch rings
Rafael Holanda, Cleto B. Miranda-Neto
We establish new results on (co)homology vanishing and Ext-Tor dualities, and derive a number of freeness criteria for finite modules over Cohen-Macaulay local rings. In the main a…
Multigraded Tor and local cohomology
Marc Chardin, Rafael Holanda
Notions of Castelnuovo-Mumford regularity and of invariant were extended from standard graded algebras to the toric setting. We here focus our attention on the standard multi…
Bass and Betti numbers of a module and its deficiency modules
Thiago Fiel, Rafael Holanda
This paper aims to provide several relations between Bass and Betti numbers of a given module and its deficiency modules. Such relations and the tools used throughout allow us to g…