On Extension modules of finite homological dimension
Commutative Algebra
2026-02-11 v2
Abstract
We explore the implications of the finiteness of homological dimensions for Ext modules, focusing on projective dimension, injective dimension, and their Gorenstein counterpart. In this direction, we establish several finiteness criteria for homological dimensions. Under such finiteness conditions, our main result is a new duality for certain Ext modules when tensored by canonical modules.
Keywords
Cite
@article{arxiv.2504.15224,
title = {On Extension modules of finite homological dimension},
author = {Rafael Holanda and Victor H. Jorge-Pérez and Victor D. Mendoza-Rubio},
journal= {arXiv preprint arXiv:2504.15224},
year = {2026}
}
Comments
14 pages. Shorter version with minor corrections. Also, an addendum has been added mentioning that some posed questions have been resolved by Kaito Kimura (arXiv:2508.12843)