Non-liftability conjecture for maps into isogeny leaves

Let $Z$ be a smooth irreducible variety over $k$, and let $\varphi:Z\to I(x)$ be a nontrivial map, where $I(x)$ is an isogeny leaf. Non-liftability conjecture for maps into isogeny leaves. Then the map

$$\varphi: Z\to I(x)$$

cannot be lifted to $W(k)$. This extends the established non-liftability result for smooth quasi-projective or proper irreducible varieties to arbitrary smooth irreducible varieties; the source says that the general case is conjectural because a suitable specialization map is unavailable.