Title: Meta-abelian anabelian geometry over algebraically closed base fields

Abstract: Consider function fields K|k of transcendence degree > 1 with k algebraically closed. In my talk I will describe a strategy for recovering K from its pro-l meta-abelian Galois group in a functorial way when k is an algebraic closure of a finite field. This completes – for such base fields k – a Program started by Bogomolov at the beginning of the 1990's. Using this fact, I will further give some hints for a possible strategy which might work for algebraically closed base fields k of positive characteristic when the transcendence degree of K|k is > 2.

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