For function fields of transcendence degree at least two over algebraically closed fields of characteristic different from a fixed prime ell, two perfect-closure field isomorphisms preserving the constant fields that induce the same pro-ell abelian-by-central Galois data up to ell-adic unit scaling agree up to Frobenius.
For function fields of transcendence degree at least two over algebraically closed fields of characteristic different from a fixed prime ell, two perfect-closure field isomorphisms preserving the constant fields that induce the same pro-ell abelian-by-central Galois data up to ell-adic unit scaling agree up to Frobenius.
For function fields of transcendence degree at least two over algebraically closed fields of characteristic different from a fixed prime ell, two perfect-closure field isomorphisms preserving the constant fields that induce the same pro-ell abelian-by-central Galois data up to ell-adic unit scaling agree up to Frobenius.
If correct, identifies exactly the uniqueness ambiguity in the group-to-field reconstruction correspondence.
Can two field isomorphisms induce the same Bogomolov–Pop Galois data without agreeing up to Frobenius and scalar ambiguity?
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