A question about the definition of ample line bundle.
On a Noetherian scheme, a line bundle $L$ is said to be ample if for any coherent sheaf $F$, there exists $n_0\in\mathbb N$ such that $F\otimes L^{\otimes n}$ is globally generated for all $n\geq n_0$.
I wonder if now I know following condition, can I conclude that $L$ is ample?
for any coherent sheaf $F$, there exists $n\in\mathbb N$,depends on $F$ such that $F\otimes L^{\otimes n}$ is globally generated
That is to say, if we know for some $n_0$, $F\otimes L^{\otimes n_0}$ is globally generated, do we have that $F\otimes L^{\otimes n}$ is globally generated for sufficiently large $n$?