{"id":"openai-math/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups","pdf":"https://github.com/openai/math/blob/main/preprints/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026/open-homomorphisms-solvably-closed-galois-groups.pdf","url":"https://github.com/openai/math/tree/main/preprints/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-Groups-October-5-2026","tags":["number-theory","galois-theory","absolute-galois-group"],"score":0,"title":"Open Homomorphisms of Global Solvably Closed Galois Groups","domain":"Number theory","family":"031","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove Uchida's conjecture on open homomorphisms of Galois groups. Every continuous open homomorphism between Galois groups of solvably closed Galois extensions of number fields is induced by a unique equivariant field embedding in the opposite direction. No restriction on the kernel or additional compatibility hypothesis is required.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Uchida’s conjecture for open homomorphisms of Galois groups"}