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.

59 pages; accepted version, to appear in Selecta

References in corpus (5)

• Higher Topos Theory
• The étale local structure of algebraic stacks
• K-theory and G-theory of derived algebraic stacks
• On nilpotent extensions of $\infty$-categories and the cyclotomic trace
• Weibel's conjecture for twisted K-theory

Cited by in corpus (3)

• 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