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Algebraic K-theory of quasi-smooth blow-ups and cdh descent. (K-théorie algébrique des éclatements quasi-lisses et descente pour la topologie cdh.) (English. French summary) Zbl 07272950
Summary: 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.
MSC:
20C25 Projective representations and multipliers
14J99 Surfaces and higher-dimensional varieties
14A20 Generalizations (algebraic spaces, stacks)
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