The Stacks project

Remark 59.88.1. Let $f : X \to S$ be a morphism of schemes. Let $n$ be an integer. We will say $BC(f, n, q_0)$ is true if for every commutative diagram

\[ \xymatrix{ X \ar[d]_ f & X' \ar[l] \ar[d]_{f'} & Y \ar[l]^ h \ar[d]^ e \\ S & S' \ar[l] & T \ar[l]_ g } \]

with $X' = X \times _ S S'$ and $Y = X' \times _{S'} T$ and $g$ quasi-compact and quasi-separated, and every abelian sheaf $\mathcal{F}$ on $T_{\acute{e}tale}$ annihilated by $n$ the base change map

\[ (f')^{-1}R^ qg_*\mathcal{F} \longrightarrow R^ qh_*e^{-1}\mathcal{F} \]

is an isomorphism for $q \leq q_0$.

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