Algebraic K-theory of quasi-smooth blow-ups and cdh descent

Abstract

We construct a semi-orthogonal decomposition on the category of perfect complexes on the blow-up of a derived Artin stack in a quasi-smooth centre. This gives a generalization of Thomason's blow-up formula in algebraic K-theory to derived stacks. We also provide a new criterion for descent in Voevodsky's cdh topology, which we use to give a direct proof of Cisinski's theorem that Weibel's homotopy invariant K-theory satisfies cdh descent.

arXiv comment24 pages; to appear in Annales Henri Lebesgue

References in corpus (7)

• A universal characterization of higher algebraic K-theory
• Localization theorems in topological Hochschild homology and topological cyclic homology
• Perfect complexes on algebraic stacks
• Descente par éclatements en K-théorie invariante par homotopie
• Algebraic K-theory and descent for blow-ups
• The Morel-Voevodsky localization theorem in spectral algebraic geometry
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Cited by in corpus (8)

• Virtual Cartier divisors and blow-ups
• K-theory and G-theory of derived algebraic stacks
• Categorical Milnor squares and K-theory of algebraic stacks
• Virtual excess intersection theory
• Cohomology of the moduli stack of algebraic vector bundles
• Introduction to Framed Correspondences
• Blow-ups and normal bundles in connective and nonconnective derived geometries
• ${\mathbb{A}}^1$-invariance of localizing invariants