  We construct a canonical pseudofunctor ^# on the category of finite-type maps
of (say) connected noetherian universally catenary finite-dimensional separated
schemes, taking values in the category of Cousin complexes. This pseudofunctor
is a concrete approximation to the restriction of the Grothendieck Duality
pseudofunctor ^! to the full subcategory of the derived category having
Cohen-Macaulay complexes as objects (a subcategory equivalent to the category
of Cousin complexes, once a codimension function has been fixed). Specifically,
for Cousin complexes M and any scheme map f:X -> Y as above, there is a
functorial derived-category map \gamma: f^# M -> f^! M inducing a functorial
isomorphism in the category of Cousin complexes f^# M \iso E(f^! M) (where E is
the Cousin functor). \gamma itself is an isomorphism if the complex f^! M is
Cohen-Macaulay--which will be so whenever the map f is flat or whenever the
complex M is injective. Also, f^# takes residual (resp. injective) complexes on
Y to residual (resp. injective) complexes on X; and so the pseudofunctor ^#
generalises--and makes canonical--the "variance theory" of residual complexes
developed in Chapter VI of Hartshorne's "Residues and Duality."
  Moreover, we generalise the Residue Theorem of loc.cit., p.369 by defining a
functorial Trace map of graded modules Tr_f(M): f_*f^# M -> M (a sum of local
residues) such that whenever f is proper, Tr_f(M) is a map of complexes and the
pair (f^# M, Tr_f(M)) represents the functor Hom(f_*C, M) of Cousin complexes
C.
