## Semisimple vs ordinary trace of Frobenius on nearby cycles of affine flag variety

Let G→X be a parahoric group scheme over a curve, with parahoric level structure at x0. Gaitsgory essentially showed that the nearby cycles functor RΨ takes perverse sheaves on the affine Grassmannian GrG|X−x0 to central perverse sheaves on the affine flag variety GrG|x0=FlG. This shows that the Frobenius trace function is central in the parahoric … Read more