The local lifting problem for actions of finite groups on curves
The local lifting problem for actions of finite groups on curves
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曲线上有限群作用的局部提升问题
DOI：
10.24033/asens.2150
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
D. Harbater
中科院分区：
文献类型：
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作者：
T. Chinburg;R. Guralnick;D. Harbater
设$k$是一个特征为$p > 0$的代数闭域。研究有限群$G$对$k[[t]]$的忠实连续作用$\ φ $提升到特征0的障碍。对于每一个这样的$\ $，Katz和Gabber的一个定理将$G$作用于光滑投影曲线$Y$ / $k$。我们说，如果$G$作用于特征为0的光滑投影曲线$X$，使得$X/H$和$Y/H$对于所有子群$H \子集G$具有相同的属，则$\phi$的KGB障碍消失。我们确定克格勃对每一个$\ φ $的阻挠在哪个$G$中消失。我们还考虑了类似的问题，在这些问题中，我们只要求对于某些$\ $或对于所有充分派生的$\ $，由于Bertin而导致的对$\ $的提升障碍消失。这些结果为加强奥尔特的提升猜想提供了证据。
Let $k$ be an algebraically closed field of characteristic $p > 0$. We study obstructions to lifting to characteristic 0 the faithful continuous action $\phi$ of a finite group $G$ on $k[[t]]$. To each such $\phi$ a theorem of Katz and Gabber associates an action of $G$ on a smooth projective curve $Y$ over $k$. We say that the KGB obstruction of $\phi$ vanishes if $G$ acts on a smooth projective curve $X$ in characteristic 0 in such a way that $X/H$ and $Y/H$ have the same genus for all subgroups $H \subset G$. We determine for which $G$ the KGB obstruction of every $\phi$ vanishes. We also consider analogous problems in which one requires only that an obstruction to lifting $\phi$ due to Bertin vanishes for some $\phi$, or for all sufficiently ramified $\phi$. These results provide evidence for a strengthening of Oort's lifting conjecture.