Applications of stratifying systems to the finitistic dimension

Given an Ext-injective stratifying system of Λ-modules (θ,Y̲,≼) 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 I(θ)={X∈modΛ:ExtΛ1(-,X)|F(θ)=0}. 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.