Let $X$ be a proper geometrically integral locally complete intersection $\mathbb{F}_p$-scheme.

Assume that $X$ is the special fiber of a proper flat $\mathbb{Z}_p$-scheme with a smooth generic fiber and that for each point $x\in X$ we have $\dim_{\kappa (x)}(\Omega _{X/\mathbb{F}_p, x}\otimes_{\mathcal{O}_{X, x}} \kappa (x))\leq 1+\dim(X)$.

Is $X$ the special fiber of a regular proper flat $\mathbb{Z}_p$-scheme?