  The Springer correspondence makes a link between the characters of a Weyl
group and the geometry of the nilpotent cone of the corresponding semisimple
Lie algebra. In this article, we consider a modular version of the theory, and
show that the decomposition numbers of a Weyl group are particular cases of
decomposition numbers for equivariant perverse sheaves on the nilpotent cone.
We give some decomposition numbers which can be obtained geometrically. In the
case of the symmetric group, we show that James' row and column removal rule
for the symmetric group can be derived from a smooth equivalence between
nilpotent singularities proved by Kraft and Procesi. We give the complete
structure of the Springer and Grothendieck sheaves in the case of $SL_2$.
Finally, we determine explicitly the modular Springer correspondence for
exceptional types.

Representation Theory