The good reduction conjecture for K3 surfaces

Let $k$ be an algebraically closed field of characteristic $p>0$ and let $F$ be a finite extension of $W[1/p]$. Let $X_F$ be a K3 surface over $F$ such that \H^2_\et(X_{\bar{F}},\bQ_\ell) is unramified for some prime $\ell\ne p$. The good reduction conjecture. Then $X_F$ has potentially good reduction. This is a good-reduction statement for K3 surfaces under an unramifiedness hypothesis on second étale cohomology; the supplied text gives no evidence of resolution.