Sheaves and Algebraic Geometry

If $s_x\neq 0$ for all $x\in X$, then $\mathcal{F}$ is trivial.

If $s_x\notin \mathfrak{m}_x\mathcal{F}_x$ for all $x\in X$, then $\mathcal{F}$ is trivial.

If $\mathcal{F}$ is a line bundle (invertible sheaf), and $s_x\neq 0$ for all $x\in X$, then $\mathcal{F}$ is trivial.

If $\mathcal{F}$ is a line bundle (invertible sheaf), and $s_x\notin \mathfrak{m}_x\mathcal{F}_x$ for all $x\in X$, then $\mathcal{F}$ is trivial.