A relative Shafarevich theorem
Niels Borne
Abstract
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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