Descente propre en K-théorie invariante par homotopie, by Denis-Charles Cisinski

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 some cohomological descent theorems for homotopy invariant K-theory from the proper base change theorem in stable homotopy theory of schemes (in particular, we get descent by blow-ups in any characteristic). Gabber's uniformisation theorem implies then a vanishing theorem for homotopy invariant K-theory modulo residual torsion, which in turns gives Weibel's conjecture modulo p-torsion for schemes of characteristic p>0.

Denis-Charles Cisinski <>