Chai's Tate-linear conjecture

Let $f:X\rightarrow\mathscr{A}_{g,\mathbb{F}}^{\mathrm{ord}}$ be a map from a smooth connected variety, let $x\in X(\mathbb{F})$, and let $f^{/x}:X^{/x}\rightarrow\mathscr{A}_{g,\mathbb{F}}^{/x}$ be the induced map on formal neighborhoods. Suppose that $f$ is a locally closed immersion. Chai's Tate-linear conjecture. If $X^{/x}$ is a formal subtorus of $\mathscr{A}_{g,\mathbb{F}}^{/x}$, then $X$ is special. This is an unlikely-intersection statement on the ordinary locus of a mod $p$ Siegel modular variety; the source gives no resolution status.