Lemma 50.12.2. Let $f : X \to Y$ be a morphism of smooth proper curves over a field $k$ which satisfies the equivalent conditions of Lemma 50.12.1. If $k = H^0(Y, \mathcal{O}_ Y) = H^0(X, \mathcal{O}_ X)$ and $X$ and $Y$ have genus $g_ X$ and $g_ Y$, then

where $R \subset X$ is the effective Cartier divisor cut out by the different of $f$.

## Comments (2)

Comment #4013 by Dario Weißmann on

Comment #4123 by Johan on