a1 Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, USA (email: email@example.com)
a2 Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA (email: firstname.lastname@example.org)
a3 Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, USA (email: email@example.com)
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 A4 in characteristic two. This proves one direction of a strong form of the Oort conjecture.
(Received September 18 2007)
(Accepted January 09 2008)
2000 Mathematics subject classification