Categorical Milnor squares and K-theory of algebraic stacks

• Tom Bachmann ^[1] ; Adeel A. Khan ^[2] ; Charanya Ravi ^[3] ; Vladimir Sosnilo ^[4]
  1. [1] University of Oslo

     University of Oslo

     Noruega

     
  2. [2] Academia Sinica

     Academia Sinica

     Taiwán

     
  3. [3] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
  4. [4] University of Regensburg

     University of Regensburg

     Kreisfreie Stadt Regensburg, Alemania

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 5, 2022
• Idioma: inglés
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• Resumen

  • We introduce a notion of Milnor square of stable ∞-categories and prove a criterion under which algebraic K-theory sends such a square to a cartesian square of spectra.

    We apply this to prove Milnor excision and proper excision theorems in the K-theory of algebraic stacks with affine diagonal and nice stabilizers. This yields a generalization of Weibel’s conjecture on the vanishing of negative K-groups for this class of stacks.