Noncommutative resolutions and intersection cohomology for quotient singularities

Abstract

For a large class of good moduli spaces $X$ of symmetric stacks $\mathcal{X}$, we define noncommutative motives ${\mathbb{D}}^{\text{nc}}(X)$ which can be regarded as categorifications of the intersection cohomology of $X$. These motives are summands of noncommutative resolutions of singularities $\mathbb{D}(X)\subset D^b(\mathcal{X})$ of $X$. The category $\mathbb{D}(X)$ is a global analogue of the noncommutative resolutions of singularities of $V//G$ for $V$ a symmetric representation of a reductive group $G$ constructed by Špenko-Van den Bergh.

34 pages. Submitted

References in corpus (4)

• Semiorthogonal decompositions in algebraic geometry
• K-theoretic Hall algebras for quivers with potential
• K-Motives and Koszul Duality
• Intersection K-theory

Cited by in corpus (1)

• Intersection K-theory