# Towards Vorst's conjecture in positive characteristic

## TL;DR

This paper investigates a variant of Vorst's conjecture in positive characteristic, exploring the relationship between ring regularity and $K$-theory invariance in this setting.

## Contribution

It extends Vorst's conjecture to positive characteristic, providing new insights into $K$-theory and regularity in this context.

## Key findings

- Established a variant of Vorst's conjecture in positive characteristic.
- Connected ring regularity with $ ext{A}^1$-homotopy invariance of $K$-theory.
- Provided theoretical results supporting the conjecture in the positive characteristic case.

## Abstract

Vorst's conjecture relates the regularity of a ring with the $\mathbb{A}^1$-homotopy invariance of its $K$-theory. We show a variant of this conjecture in positive characteristic.