Moritz Kerz: Algebraic K-theory and descent for blow-ups (Lecture 2)

The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields.

Moritz Kerz: Algebraic K-theory and descent for blow-ups

Abstract:
It is well-known that special cases of descent along blow-ups for algebraic K-theory play an important role for calculating K-groups. For example Thomason proved descent for blow-ups in regular centers. However in general descent for K-theory of blow-ups does not hold. M. Morrow suggested a potential solution to this problem by considering pro-K-groups of all infinitesimal thickenings. In my lectures I will explain why this suggested form of pro-descent holds for all blow-ups of noetherian schemes and why this implies Weibel's conjecture on the vanishing of negative K-groups. This is joint work with F. Strunk and G. Tamme.