Originalversjon
Selecta Mathematica, New Series. 2022, 28 (5):85, DOI: https://doi.org/10.1007/s00029-022-00796-w
Sammendrag
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.