  In 1976, Springer defined a correspondence making a link between the
irreducible ordinary (characteristic zero) representations of a Weyl group and
the geometry of the associated nilpotent variety. In this thesis, we define a
modular Springer correspondence (in positive characteristic), and we show that
the decomposition numbers of a Weyl group (for example the symmetric group) are
particular cases of decomposition numbers for equivariant perverse sheaves on
the nilpotent variety. We calculate explicitly the decomposition numbers
associated to the regular and subregular classes, and to the minimal and
trivial classes. We determine the correspondence explicitly in the case of the
symmetric group, and show that James's row and column removal rule is a
consequence of a smooth equivalence of nilpotent singularities obtained by
Kraft and Procesi. The first chapter contains generalities about perverse
sheaves with Z_l and F_l coefficients.
