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arXiv · 1512.09112

Global Oort Groups

Ted Chinburg·Robert Guralnick·David Harbater
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Abstract

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 2p^2. We also treat the local lifting problem and relate it to the global problem.

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Ted Chinburg, Robert Guralnick, David Harbater. 2015-12-30. Global Oort Groups. https://arxiv.org/abs/1512.09112

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