Algebraic K-theory and descent for blow-ups

TL;DR

This paper proves that algebraic K-theory satisfies pro-descent for blow-up squares in noetherian schemes and applies this to confirm Weibel's conjecture on negative K-group vanishing.

Contribution

It establishes pro-descent for algebraic K-theory in the context of blow-ups and confirms a major conjecture on negative K-groups.

Findings

Pro-descent holds for algebraic K-theory in blow-up squares.

Weibel's conjecture on negative K-groups is proven.

Provides new tools for K-theory computations in algebraic geometry.

Abstract

We prove that algebraic K-theory satisfies `pro-descent' for abstract blow-up squares of noetherian schemes. As an application we derive Weibel's conjecture on the vanishing of negative K-groups.