  Feigin and Fuchs have given a well-known construction of intertwining
operators between "Fock-type" modules over the Virasoro algebra. The
intertwiners are obtained via contour integration of certain "screening
operators" over top homology classes of a configuration space. The main
observation of the present paper is that the screening operators contain more
information. Specifically, at the chain level, the screening operators provide
a certain canonical cocycle of the Virasoro (resp. affine Kac-Moody) algebra
with coefficients in the de Rham complex of an operator-valued local system on
the configuration space. This way we obtain canonical morphisms from higher
homology groups of the above local systems to appropriate higher Ext-groups
between the Fock space representations. Our construction is motivated by, and
in a special case reduces to the construction of Bowknegt et al, see [BMP1],
[BMP2].
