Algebraic K-theory of quasi-smooth blow-ups and cdh descent
Annales Henri Lebesgue, Volume 3 (2020), pp. 1091-1116.


Keywords derived algebraic geometry, semi-orthogonal decompositions, algebraic K-theory, cdh descent


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.


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