Applications of stratifying systems to the finitistic dimension

Given an Ext-injective stratifying system of Λ-modules image satisfying that the projective dimension of Y is finite, we prove that the finitistic dimension of the algebra Λ is equal to the finitistic dimension of the category image. Moreover, using the theory of stratifying systems we obtain bounds for the finitistic dimension of Λ. In particular, we get the optimal bound 2n-2 for the finitistic dimension of a standardly stratified algebra with n simples.