The global period-index conjecture for orbifolds

Let $X$ be a smooth, proper, connected orbifold, that is, a Deligne–Mumford stack of finite type with trivial generic stabilizers, of dimension $d$ over an algebraically closed field $k$. Let $\alpha\in \mathrm{H}^2_{\mathrm{\acute et}}(X,\mathbf G_m)$, with period and index defined as in the source.

Global period-index conjecture. For any such Brauer class $\alpha$,

$$\operatorname{ind}(\alpha)\divides\operatorname{per}(\alpha)^{d-1}.$$

This is a global orbifold formulation of the period-index problem. For smooth connected orbifolds, the index agrees with the index of the restriction to the function field, linking this conjecture to the field-theoretic period-index conjecture. The source gives no resolution status.