Finitistic dimension conjectures via Gorenstein projective dimension

It is a well-known result of Auslander and Reiten that contravariant finiteness the class P ∞ fin (of finitely generated modules finite projective dimension) over an Artin algebra sufficient condition for validity finitistic dimension conjectures. Motivated by fact dimensions can alternatively be computed Gorenstein dimension, we examine in this work counterpart Auslander–Reiten condition, namely GP dimension), its relation to proved implies second conjecture left artinian rings. In more special setting algebras, however, it are virtually equivalent sense any algebra, converse holds algebras which 0 modules) contravariantly finite.