Actually, the question seems quite simple but I dont figure out why it is working. Let $f$ be a non zero formal Laurent series. We want to prove that $V(f)$ (the set of $z \in \mathbb{C}^{\times}$ such that $f(z) = 0$) is a finite set.
Actually, I really wanted to use the isolated zeroes principle, but I had several problems because I don't have enough hypotheses to apply it as I wanted to do, and even if I tried hard to make it work, I did not succeed. Probably because I don't use explicitly that $f$ is a Laurent series...
Someone would have and idea ?
Thank you !
I don't think it's true. Take $\sin(z)=\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)!}z^{2n+1}$.