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Function-field reconstruction from Milnor K-theory and Galois data
Reconstructs function fields of transcendence degree at least two over algebraically closed constants from , , and their product. These data recover the perfect closure and constants when ℓ differs from the characteristic, and the original field and its named base in equal characteristic. Also proves Bogomolov–Pop reconstruction from abelian-by-central pro-ℓ Galois data away from the characteristic.
Manuscripts in this family · 3
Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory
Oct 5, 2026·mod-ell-bogomolov-pop.pdf
We prove a mod-ℓ Bogomolov–Pop reconstruction theorem for function fields of transcendence degree at least two over arbitrary algebraically closed fields of characteristic different from ℓ. The groups and , together with their full bilinear product, determine the perfect closure and its constant field. Every compatible isomorphism of these data is induced by a field isomorphism up to a single scalar in , with only Frobenius ambiguity in the field isomorphism in positive characteristic.
Reconstruction from Milnor K-theory modulo the characteristic
Oct 5, 2026·paper.pdf
Let K and L be finitely generated extensions of transcendence degree at least two over algebraically closed fields of characteristic p. We prove that every isomorphism of their first Milnor K-groups modulo p preserving the degree-two Steinberg relations is a nonzero scalar multiple of the map induced by a unique field isomorphism. The proof recovers projective lines over the subfields of pth powers by an elementary calculation with derivations.
The Bogomolov-Pop reconstruction theorem
Sep 23, 2026·paper.pdf
We prove the Bogomolov–Pop reconstruction conjecture for function fields of transcendence degree at least two over arbitrary algebraically closed fields of characteristic different from ℓ. The pro-ℓ abelian-by-central datum determines the perfect closure and its constant field, with precisely the Frobenius and ℓ-adic unit ambiguities.