5 papers · 1 filter
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…
Cox-Gorenstein algebras
Ugo Bruzzo, Rodrigo Gondim, Rafael Holanda +1
We study G-graded Artinian algebras having Poincaré duality, considering in particular their Lefschetz properties. We also prove a correspondence between the toric setup and the G…
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)…