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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