Categorical Milnor squares and K-theory of algebraic stacks

Abstract

We introduce a notion of Milnor square of stable $\infty$-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.

arXiv comment59 pages; accepted version, to appear in Selecta

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Cited by in corpus (4)

• Virtual Cartier divisors and blow-ups
• K-theory and G-theory of derived algebraic stacks
• On nilpotent extensions of $\infty$-categories and the cyclotomic trace
• ${\mathbb{A}}^1$-invariance of localizing invariants