  The global nilpotent cone N is a singular stack associated to the choice of
an algebraic group G, a smooth projective curve X, and a line bundle L on X,
which is of fundamental importance to the Geometric Langlands Program, and
which is of emerging importance to the Classical Langlands Program. In analogy
with the ordinary Springer resolution, we construct and study a resolution of
singularities of N in the special case where G=SL_2. As an immediate
application, we prove that N is equidimensional and also provide an enumeration
of its irreducible components. We hope this is the first step in constructing a
global Springer resolution for an arbitrary reductive group.
