2 citations · 3 across the 7 of their papers we have counts for
5 papers · 1 filter
Stable Under Specialization Sets and Cofiniteness
Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi
Let be a commutative noetherian ring, and a stable under specialization subset of $\Spec(R)$. We introduce a notion of -cofiniteness and study its ma…
Greenlees-May Duality in a Nutshell
Hossein Faridian
This expository article delves into the Greenlees-May Duality Theorem which is widely thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem. This…
Local homology, finiteness of Tor modules and cofiniteness
Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi
Let be an ideal of a commutative noetherian ring with unity and an -module supported at $\V(\fa)$. Let be the supermum of the integers for which $H^{\f…
Local Homology, Koszul Homology and Serre Classes
Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi
Given a Serre class of modules, we compare the containment of the Koszul homology, Ext modules, Tor modules, local homology, and local cohomology in up…
A New Outlook on Cofiniteness
Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi
Let be an ideal of a commutative noetherian (not necessarily local) ring . In the case $\cd(\mathfrak{a},R)\leq 1$, we show that the subcategory of …