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arXiv · 2011.04355

Categorical Milnor squares and K-theory of algebraic stacks

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

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Tom Bachmann, Adeel A. Khan, Charanya Ravi, Vladimir Sosnilo. 2020-11-09. Categorical Milnor squares and K-theory of algebraic stacks. https://doi.org/10.1007/s00029-022-00796-w

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