Oort groups and lifting problems

Abstract

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 two. This proves one direction of a strong form of the Oort conjecture.

Locations

• arXiv (Cornell University) - View - PDF
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• Compositio Mathematica - View - PDF