  For a separated scheme $X$ of finite type over a perfect field $k$ of
characteristic $p>0$ which admits an immersion into a proper smooth scheme over
the truncated Witt ring $W_{n}$, we define the bounded derived category of
locally finitely generated unit $F$-crystals with finite Tor-dimension on $X$
over $W_{n}$, independently of the choice of the immersion. Then we prove the
anti-equivalence of this category with the bounded derived category of
constructible \'etale sheaves of ${\mathbb Z}/{p^{n}{\mathbb Z}}$-modules with
finite Tor dimension. We also discuss the relationship of $t$-structures on
these derived categories when $n=1$. Our result is a generalization of the
Riemann-Hilbert correspondence for unit $F$-crystals due to Emerton-Kisin to
the case of (possibly singular) embeddable algebraic varieties in
characteristic $p>0$.
