Dolgachev's conjecture on $p$-power orders in Cremona groups

Let $k$ be a field of characteristic $p>0$, and let $\mathrm{Cr}_n(k)=\mathrm{Bir}_k(\mathbb{P}^n_k)$ be the Cremona group of birational automorphisms of projective $n$-space. An element has $p$-power order if its order is $p^s$ for some integer $s>0$. Dolgachev's conjecture. The Cremona group $\mathrm{Cr}_n(k)$ does not contain elements of order $p^s$ for $s>n$. This conjecture concerns the possible torsion in Cremona groups over fields of positive characteristic; the source gives no resolution status.