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

DOI10.5802/AHL.55arXiv1810.12858MaRDI QIDQ6308993

Publication date: 30 October 2018

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.

Mathematics Subject Classification ID

Projective representations and multipliers (20C25) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) (K)-theory of schemes (19E08) Motivic cohomology; motivic homotopy theory (14F42) Generalizations (algebraic spaces, stacks) (14A20) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35) Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) (14A30)

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