On Zariski's Cancellation Problem in positive characteristic

TL;DR

This paper proves that affine spaces over fields of positive characteristic are not cancellative for dimensions greater than two, addressing a longstanding problem in algebraic geometry.

Contribution

It demonstrates the non-cancellativity of affine spaces in positive characteristic for all dimensions greater than two, extending previous knowledge.

Findings

Affine space A^n_k is not cancellative for n > 2 in positive characteristic.

Addresses Zariski's Cancellation Problem in positive characteristic.

Provides new insights into algebraic geometry over fields with positive characteristic.

Abstract

In this paper we shall show that when k is a field of positive characteristic the affine space A^n_k is not cancellative for any n greater than 2.