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arXiv · 0709.0284

Oort groups and lifting problems

Ted Chinburg·Robert Guralnick·David Harbater
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Abstract

Let k be an algebraically closed field of positive characteristic p. We consider which finite groups G have the property that every faithful action of G on a connected smooth projective curve over k lifts to characteristic zero. Oort conjectured that cyclic groups have this property. We show that if a cyclic-by-p group G has this property, then G must be either cyclic or dihedral, with the exception of A_4 in characteristic 2. This proves one direction of a strong form of the Oort Conjecture.

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Ted Chinburg, Robert Guralnick, David Harbater. 2007-09-03. Oort groups and lifting problems. https://doi.org/10.1112/s0010437x08003515

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