The Galois theory of function fields over algebraically closed fields
-- Aaron Silberstein, April 15, 2016
<p>
Given the absolute Galois group of the function field F of a variety
defined over an algebraically closed field, what can we say about the
field F?  If our algebraically closed field is
<span style="text-decoration: overline">Q</span>
or
<span style="text-decoration: overline">F</span><sub>p</sub>, and the
dimension of the variety is &ge; 2, we can say, in a very real sense,
everything. This is F. Bogomolov's program of anabelian geometry.  We
discuss recent progress and new directions.