Special unipotent groups are split

TL;DR

This paper proves that over any field, a smooth unipotent algebraic group is special precisely when it is split over that field, establishing a clear criterion for their classification.

Contribution

It provides a complete characterization of special unipotent groups as exactly the split ones over any field.

Findings

Unipotent algebraic groups are special iff they are split.

The result holds over arbitrary fields.

Clarifies the structure of unipotent groups in algebraic geometry.

Abstract

We show that over any field $k$, a smooth unipotent algebraic $k$-group is special if and only if it is $k$-split.