Perversity of coinvariants of affine Springer sheaves

Abstract

Using techniques of [BKV], we construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the regular-semisimple bounded locus of the loop group LG and prove that the derived $\tau$-coinvariants of affine Grothendieck--Springer sheaves are perverse. Our main new ingredient is a theorem of Yun on compatibility of actions.