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Khan, Adeel A.

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 1520.14047

Ann. Henri Lebesgue 3, 1091-1116 (2020).
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.

Cited in 4 Documents

MSC:

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

Keywords:

derived algebraic geometry; semi-orthogonal decompositions; algebraic K-theory; cdh descent
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\textit{A. A. Khan}, Ann. Henri Lebesgue 3, 1091--1116 (2020; Zbl 1520.14047)
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References:

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