Resumen de Categorical Milnor squares and K-theory of algebraic stacks

Tom Bachmann, Adeel A. Khan, Charanya Ravi, Vladimir Sosnilo

• 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.