Algebraic K-theory and descent for blow-ups

Abstract

We prove that algebraic K-theory satisfies `pro-descent' for abstract blow-up squares of noetherian schemes. As an application we derive Weibel's conjecture on the vanishing of negative K-groups.

arXiv comment48 pages, final version

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Cited by in corpus (17)

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• K-theory and G-theory of derived algebraic stacks
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• Towards a non-archimedean analytic analog of the Bass-Quillen conjecture
• Categorical Milnor squares and K-theory of algebraic stacks
• Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces
• Purity in chromatically localized algebraic $K$-theory
• Towards Vorst's conjecture in positive characteristic
• Weibel's conjecture for twisted K-theory
• Deformation theory of perfect complexes and traces
• K-theory of admissible Zariski-Riemann spaces
• Continuous K-Theory and Cohomology of Rigid Spaces
• Prismatic Kunz's theorem
• On line bundles in derived algebraic geometry
• Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory
• K-theory of non-archimedean rings II
• Blow-ups and normal bundles in connective and nonconnective derived geometries