Ledet's essential dimension conjecture for cyclic p-groups

Let $k$ be a field of characteristic $p>0$, let $n$ be a natural number, and let $\mathrm{C}_{p^n}$ be a cyclic group of order $p^n$. Ledet's conjecture.

$$\operatorname{ed}_k(\mathrm{C}_{p^n})=n.$$

This conjecture concerns the essential dimension of cyclic $p$-groups in positive characteristic. It holds for $n=1$ and $n=2$, but remains open for every $n\geqslant 3$.