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1 results

  • Cohomological and motivic inclusion–exclusion

  • Part of
  • Ronno Das, Sean Howe
  • Journal:
    Compositio Mathematica / Volume 160 / Issue 9 / September 2024
    Published online by Cambridge University Press:
    13 September 2024, pp. 2228-2283
    Print publication:
    September 2024
    • Article
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  • We categorify the inclusion–exclusion principle for partially ordered topological spaces and schemes to a filtration on the derived category of sheaves. As a consequence, we obtain functorial spectral sequences that generalize the two spectral sequences of a stratified space and certain Vassiliev-type spectral sequences; we also obtain Euler characteristic analogs in the Grothendieck ring of varieties. As an application, we give an algebro-geometric proof of Vakil and Wood's homological stability conjecture for the space of smooth hypersurface sections of a smooth projective variety. In characteristic zero this conjecture was previously established by Aumonier via topological methods.