Valuation of a rational differential
= Valuation of a rational differential
{title2=$\nu_p(\omega)$}
If $t$ is a <uniformizer> at a point $p$ of a <smooth projective curve> and a nonzero rational differential is $\omega=f(t)\,dt$, then $\nu_p(\omega)=\nu_p(f)$. This integer is independent of the chosen uniformizer. Its positive and negative values are respectively the orders of the zero and pole of $\omega$ at $p$.