Uchida’s conjecture for open homomorphisms of Galois groups
What the paper claims, in its own words
Proves Uchida's conjecture: every continuous open homomorphism between Galois groups of possibly infinite solvably closed Galois extensions of number fields comes from a unique equivariant field embedding in the opposite direction. No restriction on the kernel or separate cyclotomic-compatibility assumption is needed.
The plain-language explainer for this entry is still coming.