Global Oort groups

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• 作者：Ted Chinburg^a ; ^{ted@math.upenn.edu} ; Robert Guralnick^b ; ^{guralnic@usc.edu} ; David Harbater^a ; ^{harbater@math.upenn.edu}
• 关键词：primary ; 20B25 ; 12F10 ; 14H37 ; secondary ; 13B05 ; 14D15 ; 14H30
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：473
• 期：Complete
• 页码：374-396
• 全文大小：509 K
• 卷排序：473

文摘

We study the Oort groups for a prime p, i.e. finite groups G such that every G-Galois branched cover of smooth curves over an algebraically closed field of characteristic p lifts to a G-cover of curves in characteristic 0. We prove that all Oort groups lie in a particular class of finite groups that we characterize, with equality of classes under a conjecture about local liftings. We prove this equality unconditionally if the order of G   is not divisible by 2p22p2. We also treat the local lifting problem and relate it to the global problem.