Lemma 44.6.2. Let $k$ be a field. Let $X$ be a smooth projective curve over $k$ with a $k$-rational point $\sigma$. For a scheme $T$ over $k$, consider the subset $F(T) \subset \mathrm{Pic}_{X/k, \sigma }(T)$ consisting of $\mathcal{L}$ such that $Rf_{T, *}\mathcal{L}$ is isomorphic to an invertible $\mathcal{O}_ T$-module placed in degree $0$. Then $F \subset \mathrm{Pic}_{X/k, \sigma }$ is a subfunctor and the inclusion is representable by open immersions.

Proof. Immediate from Derived Categories of Schemes, Lemma 36.32.3 applied with $i = 0$ and $r = 1$ and Schemes, Definition 26.15.3. $\square$

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