MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm asking this question as a follow up to the Felipe Voloch's answer to this question:

Subfields of a function field

which you can read it here:

Subfields of a function field

(I just didn't have much faith in attracting attention to an already-answered question, so I started a new one).

So, my question is that I have no idea why the mentioned algorithm works? Basically how one proves that every subfield of $F$ corresponds to a subspace of the space of Global homomorphic differentials of $F$. Unfortunately, the "(proof left to the reader)", didn't worked out for me.

I would be more than grateful, if you suggest me a reference that helps me to tackles the math behind the algorithm.

share|cite|improve this question
Not every subspace correspond to a (proper) subfield. But you get a subspace from a subfield by looking at the pullbacks of the holomorphic differentials of the subfield. I was just using the fact that, for a non-hyperelliptic curve, the canonical morphism is an embedding. This is all in Hartshorne. – Felipe Voloch Aug 10 '11 at 23:40

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.