Cyclic Covers over Strongly Liftable Schemes

Qihong Xie

paper

Cyclic Covers over Strongly Liftable Schemes

arXiv:1401.3064

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 $W_{2} (k)$ .

10 pages. arXiv admin note: text overlap with arXiv:1301.0857