Let $X$ be an arithmetic surface and $f\in K(X)$ be a function in the function field. Is there any analagous "product formula" showing $\deg(f)=0$? This is motivated by the number field case, where $X=Spec(\mathcal{O}_{K})$ and $f\in K$ is an element in the number field.
$\begingroup$
$\endgroup$
Add a comment
|