Modular perverse sheaves on symplectic singularities
A symplectic singularity has a natural stratification by Poisson leaves, which are symplectic, hence even-dimensional. Perverse sheaves constructible with respect to this stratification are semisimple if the coefficients are in characteristic zero, but with characteristic p coefficients the categories can be complicated. I will discuss two cases where this category has been understood. For the nilpotent cone of GL(n)GL(n), Mautner showed that perverse sheaves are equivalent to representations of a Schur algebra S(n,n)S(n,n), which is a highest weight category and is its own Ringel dual. In joint work with Mautner, we showed that perverse sheaves on an affine hypertoric variety form a highest weight category which is Ringel dual to the same category for the symplectic dual hypertoric variety. Time permitting, I will discuss what might be true for other symplectic singularities.