{"id":"openai-math/Reconstruction-from-Milnor-K-theory-modulo-the-characteristic","pdf":"https://github.com/openai/math/blob/main/preprints/Reconstruction-from-Milnor-K-theory-modulo-the-characteristic-October-5-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Reconstruction-from-Milnor-K-theory-modulo-the-characteristic-October-5-2026","tags":["algebra","field-theory","k-theory"],"score":0,"title":"Reconstruction from Milnor K-theory modulo the characteristic","domain":"Number theory","family":"009","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"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 p th powers by an elementary calculation with derivations.","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"}