The K-theory of toric varieties in positive characteristic

TL;DR

This paper proves that for toric schemes over regular rings with a field, the direct limit of their K-groups under dilations is homotopy invariant, extending known results from characteristic zero to positive characteristic.

Contribution

It establishes the homotopy invariance of K-groups for toric schemes over regular rings in positive characteristic, confirming a conjecture by Gubeladze in the affine case.

Findings

Homotopy invariance of K-groups under dilations in positive characteristic

Extension of known characteristic zero results to positive characteristic

Affirmation of Gubeladze's conjecture in the affine case

Abstract

We show that if X is a toric scheme over a regular ring containing a field then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was known in characteristic 0. The affine case of our result was conjectured by Gubeladze.