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Categorical Milnor squares and K-theory of algebraic stacks

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


We introduce a notion of Milnor square of stable infinity-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.

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