  In this paper we construct some quantum analogues of the global Cousin
complex for the flag variety in positive characteristic. Just like in the
positive characteristic case, we obtain some remarkable resolutions of the
contragradient modules over the small quantum group. We use these resolutions
to calculate semiinfinite cohomology of the small quantum group with
coefficients in contragradient Weyl modules. It turns out that the described
graded space of semiinfinite cohomology is naturally isomorphic to the space of
distributions on the cotangent bundle of the flag variety with support in the
union of conormal bundles to the Schubert cells with coefficients in the
pull-back of a line bundle on the flag variety.
