The dimension bound conjecture for torsion motives

Let $M=(X,\rho)$ be a torsion motive of $p$-level $n$.

Dimension bound conjecture. Then

$$\operatorname{dim}(X)\geqslant \left\lceil\frac{n}{2}\right\rceil+\frac{p^{n}-1}{p-1}.$$

This is proposed in light of expected properties of Chow motives, in particular the Rost nilpotence conjecture. The bound is established in the preceding corollary when $k=\overline{k}$ and $n\leqslant 4$, while the general assertion remains open.