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 the factors of a nonzero reflexive tensor product of finitely generated modules over hypersurface rings can be 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. [ABSTRACT FROM AUTHOR]