Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Oort groups and lifting problems   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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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg