Strong Probability On W (k)

Let k be an algebraically closed field of characteristic p>0and W(k) the ring of Witt vectors of k. A smooth scheme X over k is called a strongly liftable scheme over W(k), if X and all prime divisors on X can be lifted simultaneously over W(k). In my master thesis, I study explicitly some properties of strongly liftable schemes over W(k); give a criterion for strongly liftable schemes over W(k); prove that affine spaces, projective spaces, smooth projective curves, smooth projective rational surfaces, some smooth complete intersection subschemes in projective spaces and smooth projective toric varieties are strongly liftable over W(k). In addition, I study some properties of cyclic covers over W(k), and obtain a large class of smooth projective varieties which are liftable over W(k).