# Adeel Khan (Regensburg): A criterion for descent by blow-ups

Unlike most cohomology theories in algebraic geometry, algebraic K-theory
does not satisfy descent with respect to arbitrary blow-up squares. We
explain why the only obstruction is the failure of the Mayer-Vietoris
property for unions of closed subschemes. Since this obstruction vanishes
after forcing A^{1}-homotopy invariance, this gives a direct new proof of
Cisinski's theorem that homotopy K-theory does satisfy cdh descent.

Published Apr. 23, 2019 5:32 PM
- Last modified Apr. 23, 2019 5:32 PM