Descente par éclatements en K-théorie invariante par homotopie

Abstract

These notes give a proof of the representability of homotopy invariant K-theory in the stable homotopy category of schemes (which was announced by Voevodsky). One deduces from the proper base change theorem in stable homotopy theory of schemes a descent by blow-ups theorem for homotopy invariant K-theory.

in French; final version

References in corpus (1)

• Algebraic K-theory, A^1-homotopy and Riemann-Roch theorems

Cited by in corpus (16)

• The six operations in equivariant motivic homotopy theory
• Étale motives
• Topological K-theory of complex noncommutative spaces
• Algebraic K-theory and descent for blow-ups
• Perfection in motivic homotopy theory
• K-theory and G-theory of derived algebraic stacks
• Algebraic K-theory of quasi-smooth blow-ups and cdh descent
• Vanishing of negative $K$-theory in positive characteristic
• Framed transfers and motivic fundamental classes
• Differential forms in positive characteristic II: cdh-descent via functorial Riemann-Zariski spaces
• Purity in chromatically localized algebraic $K$-theory
• Algebraic Cobordism and Étale Cohomology
• Towards Vorst's conjecture in positive characteristic
• The homotopy limit problem and the cellular Picard group of Hermitian $K$-theory
• The cdh-local motivic homotopy category
• Trace maps in motivic homotopy and local terms