On the essential dimension of unipotent algebraic groups

TL;DR

This paper establishes an upper bound for the essential dimension of smooth unipotent algebraic groups over any field and characterizes when such groups have essential dimension zero over finitely generated fields.

Contribution

It provides a new upper bound for the essential dimension of smooth unipotent algebraic groups and characterizes those with zero essential dimension over finitely generated fields.

Findings

Upper bound for essential dimension of smooth unipotent groups

Characterization of groups with essential dimension zero over finitely generated fields

Equivalence of being $k$-split and having essential dimension zero

Abstract

We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field $k$ which is finitely generated over a perfect field, a smooth unipotent algebraic $k$-group is of essential dimension 0 if and only if it is $k$-split.