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Open Homomorphisms of Global Solvably Closed Galois Groups

OpenAI

OpenAI Mathopenai-math/Open-Homomorphisms-of-Global-Solvably-Closed-Galois-GroupsOct 5, 2026math.NTAI-generatedscore 0

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.

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