Categorical Milnor squares and K-theory of algebraic stacks
Algebraic Geometry
2024-09-24 v3 K-Theory and Homology
Abstract
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.
Keywords
Cite
@article{arxiv.2011.04355,
title = {Categorical Milnor squares and K-theory of algebraic stacks},
author = {Tom Bachmann and Adeel A. Khan and Charanya Ravi and Vladimir Sosnilo},
journal= {arXiv preprint arXiv:2011.04355},
year = {2024}
}
Comments
59 pages; accepted version, to appear in Selecta