On the vanishing of negative homotopy K-theory

TL;DR

This paper proves that the homotopy invariant algebraic K-theory of noetherian schemes vanishes below a certain negative degree, supporting Weibel's conjecture on negative algebraic K-groups.

Contribution

It establishes a vanishing result for homotopy invariant algebraic K-theory below the negative of the scheme's dimension, providing evidence for Weibel's conjecture.

Findings

Homotopy invariant algebraic K-theory vanishes below negative dimension

Supports Weibel's conjecture on negative K-groups

Provides a new vanishing criterion for noetherian schemes

Abstract

We show that the homotopy invariant algebraic K-theory of Weibel vanishes below the negative of the Krull dimension of a noetherian scheme. This gives evidence for a conjecture of Weibel about vanishing of negative algebraic K-groups.