The Stacks project

Lemma 108.5.11. Let $f : X \to B$ and $\mathcal{F}$ be as in the introduction to this section. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. Then

\[ \mathrm{Quot}^{P, \mathcal{L}}_{\mathcal{F}/X/B} = \mathrm{Quot}^{P', \mathcal{L}^{\otimes n}}_{\mathcal{F}/X/B} \]

where $P'(t) = P(nt)$.

Proof. Follows immediately after unwinding all the definitions. $\square$

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