On Extension modules of finite homological dimension

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.

arXiv comment14 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)