  Hochster's theta invariant is defined for a pair of finitely generated
modules on a hypersurface ring having only an isolated singularity. Up to a
sign, it agrees with the Euler invariant of a pair of matrix factorizations.
  Working over the complex numbers, Buchweitz and van Straten have established
an interesting connection between Hochster's theta invariant and the classical
linking form on the link of the singularity. In particular, they establish the
vanishing of the theta invariant if the hypersurface is even-dimensional by
exploiting the fact that the (reduced) cohomology of the Milnor fiber is
concentrated in odd degrees in this situation.
  In this paper, we give purely algebraic versions of some of these results. In
particular, we establish the vanishing of the theta invariant for isolated
hypersurface singularities of odd dimension in characteristic p > 0, under some
mild extra assumptions. This confirms, in a large number of cases, a conjecture
of Hailong Dao.
