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arXiv · 1301.0857

Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic III

Qihong Xie·Jian Wu
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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 first deduce the Kummer covering trick over W_2(k), which can be used to construct a large class of smooth projective varieties liftable over W_2(k), and to give a direct proof of the Kawamata-Viehweg vanishing theorem on strongly liftable schemes. Secondly, we generalize almost all of the results in [Xie10, Xie11] to the case where everything is considered over W(k), the ring of Witt vectors of k.

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Qihong Xie, Jian Wu. 2013-01-05. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic III. https://arxiv.org/abs/1301.0857

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