Good and bad Koszul algebras and their Hochschild homology (Q2570678)

A systematic study of the homological behavior of finitely and lineraly presented modules over Koszul algebras is presented. It is shown that the generating series of the linear Betti numbers of these modules over some Koszul algebras are rationally related to the generating series for the Betti numbers of all local commutative Noetherian rings. It is shown that there are very small commutative Koszul algebras for which the rational generating series for Betti numbers of linearly presented modules over them can not be put on a common denominator.