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COMPARISON OF VIEWS ON FINITISTIC PROJECTIVE DIMENSION

The finitistic dimension conjecture says that the projective dimension of finitely generated modules over an Artin algebra is bounded when finite. The conjecture is known for algebras of representation dimension 3, for modules of Loevey length 2 and for stratifying systems with at most 2 indecomposable modules of infinite projective dimension (Huard, Lanzilotta, Mendoza [4]). We would like to increase these numbers by one. We will look at stratifying systems of size 3 and examine the corresponding subquivers, Koszul dual systems for the representation dimension 4 case and the advantages of reduction to the case of finite fields. In some cases the corresponding statements are easier to solve and I will show how this works for the self-dual zero relation case. This is joint work with Gordana Todorov.