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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