Lemma 45.12.2. In the situation above. Let $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $\mathcal{E}_ i$ be a finite collection of locally free $\mathcal{O}_ X$-modules of rank $r_ i$. There exists a morphism $p : P \to X$ in $\mathcal{C}$ such that

$p^* : A(X) \to A(P)$ is injective,

each $p^*\mathcal{E}_ i$ has a filtration whose successive quotients $\mathcal{L}_{i, 1}, \ldots , \mathcal{L}_{i, r_ i}$ are invertible $\mathcal{O}_ P$-modules.

## Comments (0)