A relative Shafarevich theorem

Mathematics – Algebraic Geometry

Scientific paper

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13 pages

Scientific paper

Suppose given a Galois etale cover Y -> X of proper non-singular curves over
an algebraically closed field k of prime characteristic p. Let H be its Galois
group, and G any finite extension of H by a p-group P. We give necessary and
sufficient conditions on G to be the Galois group of an etale cover of X
dominating Y -> X.

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