Proposition 103.11.6. Let $f : \mathcal{U} \to \mathcal{X}$ be a morphism of algebraic stacks. Assume $f$ is representable by algebraic spaces, surjective, flat, and locally of finite presentation. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_\mathcal {X}$-module. Then there is a spectral sequence
\[ E_2^{p, q} = H^ q(\mathcal{U}_ p, f_ p^*\mathcal{F}) \Rightarrow H^{p + q}(\mathcal{X}, \mathcal{F}) \]
where $f_ p$ is the morphism $\mathcal{U} \times _\mathcal {X} \ldots \times _\mathcal {X} \mathcal{U} \to \mathcal{X}$ ($p + 1$ factors).
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