The derived-equivalence conjecture for Calabi–Yau threefolds

Let $X$ and $Y$ be Calabi–Yau threefolds, and write $D(X)$ and $D(Y)$ for their bounded derived categories. Derived-equivalence conjecture for Calabi–Yau threefolds. If

$$D(X)\simeq D(Y),$$

then $X$ is deformation equivalent to a birational model of $Y$. This conjecture concerns whether derived-equivalent Calabi–Yau threefolds must be related geometrically; the supplied text gives no evidence that it has been resolved.