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| A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W2(k). In this paper, first the author proves that smooth toric varieties are strongly liftable, hence the Kawamata-Viehweg vanishing theorem holds for smooth projective toric varieties. Second, the author proves the Kawamata-Viehweg vanishing theorem for normal projective surfaces which are birational to a strongly liftable smooth projective surface. Finally, the author deduces the cyclic cover trick over W2(k), which can be used to construct a large class ofliftable smooth projective varieties. |
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| Keywords:Algebraic geometry; positive characteristic; strongly liftable scheme; toric variety; Kawamata-Viehweg vanishing theorem; cyclic cover |
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