The Bogomolov-Pop conjecture in birational anabelian geometry asserts that the perfect closure of a function
field of transcendence degree at least
2 over an algebraically closed field
can be reconstructed from the abelian-by-central quotient of its maximal pro-
absolute Galois group, for a prime
number 
different from the characteristic. The quotient
retains the abelianization and its commutator
pairing. It is smaller than the full absolute Galois
group.
Bogomolov-Pop Conjecture
See also
Abelianization, Function Field, Galois Group, Milnor K-Theory, Perfect Closure, Profinite Group, Transcendence DegreeExplore with Wolfram|Alpha
References
Topaz, A. "Reconstructing Function Fields from Rational Quotients of Mod-
Galois Groups." Math. Ann. 366, 337-385,
2016. https://doi.org/10.1007/s00208-015-1327-4.
Cite this as:
Weisstein, Eric W. "Bogomolov-Pop Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Bogomolov-PopConjecture.html