• Corpus ID: 119724669

The integrality conjecture and the cohomology of preprojective stacks

  title={The integrality conjecture and the cohomology of preprojective stacks},
  author={Ben Davison},
  journal={arXiv: Algebraic Geometry},
  • Ben Davison
  • Published 5 February 2016
  • Mathematics
  • arXiv: Algebraic Geometry
By importing the compactly supported cohomology of various stacks of representations of the preprojective algebra $\Pi_Q$, for $Q$ an arbitrary quiver, into the theory of cohomological Donaldson--Thomas invariants, we prove that this cohomology is pure. In addition, we prove a generalisation of Hausel's formula for the Betti numbers of Nakajima quiver varieties, a degeneration result for preprojective cohomological Hall algebras with extra equivariant parameters, and calculate the mixed Hodge… 
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