Descente par éclatements en $K$-théorie invariante par homotopie

Abstract

Ces notes donnent une preuve de la représentabilité de la $K$-théorie invariante par homotopie dans la catégorie homotopique stable des schémas (résultat annoncé par Voevodsky). On en déduit, grâce au théorème de changement de base propre en théorie de l’homotopie stable des schémas, un théorème de descente par éclatements en $K$-théorie invariante par homotopie.

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.

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Authors

Denis-Charles Cisinski

Université Paul Sabatier
Institut de Mathématiques de Toulouse
Toulouse
France