Cyclic Covers over Strongly Liftable Schemes

Abstract

A smooth scheme $X$ over a field $k$ of positive characteristic is said to be strongly liftable over $W_2(k)$, if $X$ and all prime divisors on $X$ can be lifted simultaneously over $W_2(k)$. In this paper, we give a criterion for that cyclic covers over strongly liftable schemes are still strongly liftable. As a corollary, cyclic covers over projective spaces of dimension at least three are strongly liftable over $W_2(k)$.