Perverse sheaves on infinite-dimensional stacks, and affine Springer theory

The goal of this work is to construct a perverse t-structure on the ∞-category of ℓ-adic LG-equivariant sheaves on the loop Lie algebra Lg and to show that the affine Grothendieck–Springer sheaf S is perverse. Moreover, S is an intermediate extension of its restriction to the locus of “compact” elements with regular semi-simple reduction. Note that classical methods do not apply in our situation because LG and Lg are infinite-dimensional ind-schemes.