A generalization of the Oort Conjecture
A generalization of the Oort Conjecture
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奥尔特猜想的推广
DOI：
10.4171/cmh/419
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Andrew Obus
中科院分区：
文献类型：
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作者：
Andrew Obus
奥尔特猜想（现为Obus-Wewers和Pop的定理）指出，如果k是特征为p的代数闭域，则光滑射影k曲线的任何循环分支覆盖都提升到特征为零。这等价于局部奥尔特猜想，即k[[t]]的所有循环扩展都提升到特征零。我们将局部Oort猜想推广到具有循环p- sylow子群的伽罗瓦扩展情况，将该猜想简化为一个纯特征p命题，并在若干情况下证明了它。特别地，我们证明D_9是一个所谓的本地奥尔特群。
The Oort conjecture (now a theorem of Obus-Wewers and Pop) states that if k is an algebraically closed field of characteristic p, then any cyclic branched cover of smooth projective k-curves lifts to characteristic zero. This is equivalent to the local Oort conjecture, which states that all cyclic extensions of k[[t]] lift to characteristic zero. We generalize the local Oort conjecture to the case of Galois extensions with cyclic p-Sylow subgroups, reduce the conjecture to a pure characteristic p statement, and prove it in several cases. In particular, we show that D_9 is a so-called local Oort group.