| Résume | Rational Gorenstein singularities in dimension 2 can be realized, under minor assumptions on the base characteristic, inside the nilpotent cone of a simple Lie algebra. Using ideas dating back to Borho, MacPherson and Slodowy, one can resolve such singularities in families using the Grothendieck--Brieskorn resolution and re-derive Springer's construction of irreducible Weyl group representations on the cohomology of Springer fibers. In this talk we will explain a mixed-characteristic incarnation of this construction to study 1-parameter degenerations to these "generic" singularities of the nilpotent cone, and relate it to the theory of nearby cycles over a large base. Time permitting, we will see how that method extends to studying singularities appearing in lower strata of the nilpotent cone (aka generic singularities of nilpotent orbit closures). |
