Uchida's homomorphism conjecture asserts that open homomorphisms between the Galois groups of solvably closed Galois extensions of number
fields recover unique field embeddings in the opposite
direction. Let 
be possibly infinite Galois
extensions, where 
is a number field and 
is solvably closed. For every continuous homomorphism with open image
 |
the assertion is that there is a unique embedding 
with
 |
for every 
. Such an embedding sends 
into 
.
