Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 009-01. Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory
Manuscript map · lines 2585–2594
OpenAI@2026-10-07#rem:oai-p-009-01
Authors: OpenAI. Family 009.
Title: Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory.
Abstract: 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 $K{}{{}mathrm M}_1/{}ell$ and $K{}{{}mathrm M}_2/{}ell$, 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 ${}mathbb F_{}ell{}{}times$, with only Frobenius ambiguity in the field isomorphism in positive characteristic.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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