  We observe that on the level of derived categories, representations of the
Lie algebra of a semisimple algebraic group over a field of characteristic $p>
h$ (where $h$ is the Coxeter number), with a given (generalized) central
character are the same as the coherent sheaves on (generalized) Springer
fibers.
  The first step is to observe that the derived functor of global sections
provides an equivalence between the derived category of $D$-modules (with no
divided powers) on the flag variety and the appropriate derived category of
modules over the corresponding Lie algebra. Thus the ``derived'' version of the
Beilinson-Bernstein localization Theorem holds in sufficiently large positive
characteristic. Next, the algebra of (``crystalline'') differential operators
is an Azumaya algebra and its splittings on Springer fibers allow us to pass
from D-modules to coherent sheaves. As an application we compute the rank of
the Grothendieck group of the category of modules over the Lie algebra with a
fixed central character.
