We show that the conjecture of Oort on lifting covers of curves is true. The main ingredients in the proof are a deformation argument in characteristic p and (a special case of) a very recent result by Obus-Wewers. A kind of boundedness result is given as well.
In this article we introduce and prove a Z/p meta-abelian form of the birational p-adic section conjecture for curves. This is a much stronger result than the usual p-adic birational section conjecture for curves, and makes an effective p-adic section conjecture for curves quite plausible.
In this note we show that the quotient field of a domain which is Henselian with respect to a nontrivial ideal is a large field, and give some applications of this fact, using a specialization theorem for ramified covers of the line over (generalized) Krull fields.
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