Year 12s: what will be the first way you research your future options? >>

If a morphism of curves induces Galois extension of function fields, does the galois

Suppose

f:X \rightarrow Y

is a non-constant morphism of smooth projective curves defined over an algebraically closed field. Suppose that the corresponding field extension

K(X)/K(Y)

is Galois.

Does

\text{Gal}(K(X)/K(Y))

act transitively on the fibers of

f

?

More specifically if

f(P)=f(Q)

then is there a

g \in \text{Gal}(K(X)/K(Y)

such that the induced automorphism

\sigma_g

X

maps

P

Q

?

I would just like a hint if possible something for me to ponder about thanks!

Reply 1

the bear

@ghostwalker

@DFranklin

Reply 2

ghostwalker

Original post by the bear

@ghostwalker

I can usually at least understand the question, even if I can't necessarliy help, but not that one.

DFranklin, or @RichE are the two who spring to mind as most likely to be able to assist.

(edited 6 years ago)

Reply 3

poorform

Thanks for looking but I have an email from my professor now so it is understood.

Typical I post on stack and email him wait and hear nothing back post on here and then he gets back to me haaaa.

Reply 4

DFranklin

Original post by ghostwalker

I can usually at least understand the question, even if I can't necessarliy help, but not that one.

DFranklin, or @RichE are the two who spring to mind as most likely to be able to assist.

Yeah, past my competence too, I'm afraid...