  We construct a complex of free-modules over a Gorenstein ring R of dimension
five, for which the Euler characteristic and Dutta multiplicity are different.
This complex is the resolution of an R-module of finite length and finite
projective dimension. As a consequence, the ring R has a nonzero Todd class
tau_3(R) and a bounded free complex whose local Chern character does not vanish
on this class.
  In the course of our work, we construct a module N of finite length and
finite projective dimension over the hypersurface A=K[u,v,w,x,y,z]/(ux+vy+wz),
such that the Serre intersection multiplicity of the modules N and A/(u,v,w)A
is -2.
