Jannsen's vanishing conjecture for étale cohomology

Let $X$ be a smooth, projective scheme over ${\cal O}_K[1/S]$, and let $\bar{X}:=X\times_{{\cal O}_K[1/S]}\bar{K}$ be its base change to an algebraic closure. For integers $i$ and $j$, Jannsen's vanishing conjecture. If $i+1<j$ or $i+1>2j$, then

$$H^2({\cal O}_K[1/S],H^i(\bar{X},\mathbb{Q}_p(j)))=0.$$

The conjecture predicts the expected range of vanishing for degree-two étale cohomology and is part of Jannsen's framework relating étale, motivic, and regulator cohomology. The source gives no resolution, so its status is open.