  In math.RT/0304173 the derived category of the principal block in modules
over the Lusztig quantum algebra at a root of unity is related to the derived
category of equivariant coherent sheaves on the Springer resolution. In the
present paper we deduce a similar relation between the derived category of the
principal block for the {\em small (reduced) quantum algebra} and the derived
category of (non-equivariant) coherent sheaves on the Springer resolution. As
an application we get a geometric description of Hochschild cohomology (in
particular, the center) of the regular block for the small quantum group, and
use it to give an explicit description of a certain subalgebra in the center
(obtained previously by another method and under more restrictive assumptions
in math.QA/0107098. We also briefly explain the relation of our result to the
geometric description math.RT/0407048 of the derived category of modules over
the De Concini -- Kac quantum algebra.
