Lemma 17.25.5. Let $(X, \mathcal{O}_ X)$ be a ringed space.

If $\mathcal{L}$, $\mathcal{N}$ are invertible $\mathcal{O}_ X$-modules, then so is $\mathcal{L} \otimes _{\mathcal{O}_ X} \mathcal{N}$.

If $\mathcal{L}$ is an invertible $\mathcal{O}_ X$-module, then so is $\mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(\mathcal{L}, \mathcal{O}_ X)$ and the evaluation map $\mathcal{L} \otimes _{\mathcal{O}_ X} \mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(\mathcal{L}, \mathcal{O}_ X) \to \mathcal{O}_ X$ is an isomorphism.

## Comments (3)

Comment #9 by Pieter Belmans on

Comment #10 by Pieter Belmans on

Comment #19 by Johan on