While working on a project for mathematics I came across the following lemma: [Kock]

If $X$ is a curve defined over an algebraically closed subfield $N$ of $\mathbb{C}$ and let $t:X\rightarrow \mathbb{P}_{\mathbb{C}}^1$ be a finite morphism defined over $N$, then the critical values of $t$ are $N$-rational.

I have only recently started learning about this sort of stuff and have been utlising Forster's *Lectures on Riemann Surfaces*. I restated the theorem as follows:

If $X$ is a compact connected Riemann surface defined over an algebraically closed subfield $N$ of $\mathbb{C}$ and let $t:X\rightarrow \mathbb{P}_{\mathbb{C}}^1$ be a non-constant holomorphic map defined over $N$, then the critical values of $t$ are $N$-rational.

I believe this is allowable as compact Riemann surfaces can be embedded in a projective space where they are the common zero of a set of polynomials over $N$. (My wording here may be a little off - feel free to correct me).

Kock in his proof uses the following fact that seems simple but has me absolutely stumped (even after days of research):

The set of critical values of $t$ are given by $t(supp(\Omega_{X/\mathbb{P}_{\mathbb{C}}^1}))$

What is the definition of $supp(\Omega_{X/\mathbb{P}_{\mathbb{C}}^1})$? And how does this fact follow?