A resolution of singularities for Drinfeld’s compactification by stable maps

Abstract

Drinfeld's relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting of stable maps from nodal deformations of the curve into twisted flag varieties. As an application, we prove that the twisted intersection cohomology sheaf on Drinfeld's compactification is universally locally acyclic over the moduli stack of G-bundles at points sufficiently antidominant relative to their defect.

Nearby cycles of Whittaker sheaves on Drinfeld’s compactification

“…Thus it suffices to prove that, for sufficiently dominant, is ULA over for all . This follows immediately from [Cam16, Corollary 4.1.1.1].…”

Twisted Whittaker models for metaplectic groups

“…As in ( [23], Proposition 6.2.1), one checks that all of three are objects of Whit κ x , and the version of ( [25], Lemma 2.8) holds: Here the notationλ ′ <λ means that λ ′ i ≤ λ i for all 1 ≤ i ≤ n and for at least one i the inequality is strict. Recall that the maps (17) are not isomorphisms in general. Let DWhit κ x ⊂ D ζ ( Mx) denote the full subcategory of objects whose all perverse cohomologies lie in Whit κ x .…”