  We formulate a Beilinson-Bernstein type derived equivalence for a quantized
enveloping algebra at a root of 1 as a conjecture. It says that there exists a
derived equivalence between the category of modules over a quantized enveloping
algebra at a root of 1 with fixed regular Harish-Chandra central character and
the category of certain twisted $D$-modules on the corresponding quantized flag
manifold. We show that the proof is reduced to a statement about the (derived)
global sections of the ring of differential operators on the quantized flag
manifold. We also give a reformulation of the conjecture in terms of the
(derived) induction functor.
