Persistence of homology over commutative noetherian rings

Abstract

We describe new classes of noetherian local rings $R$ whose finitely generated modules $M$ have the property that $To{r}_i^R(M,M)=0$ for $i\gg 0$ implies that $M$ has finite projective dimension, or $Ex{t}_R^i(M,M)=0$ for $i\gg 0$ implies that $M$ has finite projective dimension or finite injective dimension.

23 pages