Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic III
Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic III
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DOI：
10.1016/j.jalgebra.2013.07.027
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发表时间：
2009-09
期刊：
影响因子：
--
通讯作者：
Qihong Xie
中科院分区：
文献类型：
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作者：
Qihong Xie
称正特征域k上的光滑概型X在W2（k）上是强提升的，如果X和X上的所有素因子都能同时在W2（k）上提升.本文首先导出了W2（k）上的库默覆盖技巧，利用它可以构造出W2（k）上的一大类光滑可提升的投射簇，并给出了强可提升格式上的Kawamata-Viehweg消失定理的一个直接证明.其次，我们将文[18]、[19]中的几乎所有结果推广到了一切都考虑在W（k）上的情形，W（k）是k的Witt向量环。
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 [18],[19] to the case where everything is considered over W (k), the ring of Witt vectors of k.