{"id":"openai-math/Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory","pdf":"https://github.com/openai/math/blob/main/preprints/Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory-October-5-2026/mod-ell-bogomolov-pop.pdf","url":"https://github.com/openai/math/tree/main/preprints/Reconstruction-of-Function-Fields-from-Mod-ell-Milnor-K-Theory-October-5-2026","tags":["algebra","field-theory","k-theory"],"score":0,"title":"Reconstruction of Function Fields from Mod-ℓ Milnor K-Theory","domain":"Number theory","family":"009","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Function-field reconstruction from Milnor K-theory and Galois data"}