Essential dimension of infinitesimal unipotent group schemes

TL;DR

This paper generalizes Ledet's conjecture to finite commutative unipotent group schemes, providing evidence and exploring implications for the essential dimension in algebraic group theory.

Contribution

It introduces a new conjecture extending Ledet's to a broader class of group schemes and discusses its potential consequences.

Findings

Proposes a generalized conjecture for essential dimension

Provides evidence supporting the conjecture

Explores implications for algebraic group schemes

Abstract

We propose a generalization of Ledet conjecture, which predicts the essential dimension of cyclic $p$-groups in characteristic $p$, for finite commutative unipotent group schemes. And we show some evidence and some consequences of this new conjecture.