On the depth and reflexivity of tensor products

In this paper we study the depth of tensor products of homologically finite complexes over commutative Noetherian local rings. As an application of our main result, we determine new conditions under which nonzero tensor products of finitely generated modules over hypersurface rings can be reflexive only if both of their factors are reflexive. A result of Asgharzadeh shows that nonzero symbolic powers of prime ideals in a local ring cannot have finite projective dimension, unless the ring in question is a domain. We make use of this fact in the appendix and consider the reflexivity of tensor products of prime ideals over hypersurface rings.

PDF Abstract