I am trying to solve the following exercise without using Zariski's main theorem. Let X be an integral scheme of dimension 1 and $f:X \rightarrow Y$ a birational, separated morphism of finite type where Y is a Dedekind scheme. Show that f is an open immersion.
It seems as if X was proper over Y, the case would be easier but apart from that, I can not aee what to do. Any hints / solutions are welcome!
