The Stacks project

Lemma 108.8.4. Assume $f_{T, *}\mathcal{O}_{X_ T} \cong \mathcal{O}_ T$ for all schemes $T$ over $B$. Then the inertia stack of $\mathcal{P}\! \mathit{ic}_{X/B}$ is equal to $\mathbf{G}_ m \times \mathcal{P}\! \mathit{ic}_{X/B}$.

Proof. This is explained in Examples of Stacks, Example 95.17.2. $\square$

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