On The Negative K-Theory of Schemes in Finite Characteristic

TL;DR

This paper investigates the negative K-theory of singular algebraic varieties over fields of positive characteristic, establishing vanishing results for K-groups below a certain degree related to the variety's dimension.

Contribution

It proves the vanishing of negative K-groups for singular varieties over fields of positive characteristic below a specific degree, advancing understanding of K-theory in this setting.

Findings

Vanishing of K_i(X) for i < -d-2 on d-dimensional varieties

Extension of negative K-theory results to positive characteristic

Provides new insights into the structure of K-theory for singular schemes

Abstract

We study the negative $K$-theory of singular varieties over a field of positive characteristic and in particular, prove the vanishing of $K_i(X)$ for $i < -d-2$ for a $k$-variety of dimension $d$.