  We define a variant of Hochster's theta pairing and prove that it is constant
in flat families of modules over hypersurfaces with isolated singularities. As
a consequence, we show that the theta pairing factors through the Grothendieck
group modulo algebraic equivalence. Moreover, our result allows us, in certain
situations, to translate the properties of the theta pairing in characteristic
zero to the characteristic p setting. We also give an application of our result
to the rigidity of Tor over hypersurfaces.

Commutative Algebra