Descente par \'eclatements en K-th\'eorie invariante par homotopie

TL;DR

This paper proves the representability of homotopy invariant K-theory within the stable homotopy category of schemes, establishing a descent by blow-ups theorem based on proper base change in stable homotopy theory.

Contribution

It provides a proof of the representability of homotopy invariant K-theory and derives a descent theorem for blow-ups in the context of stable homotopy theory of schemes.

Findings

Homotopy invariant K-theory is representable in the stable homotopy category.

A descent by blow-ups theorem for homotopy invariant K-theory is established.

Proper base change theorem underpins the descent results.

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.