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I am looking for a reference for what is stated in Srinivasan's book "Representations of Finite Chevalley Groups", which is apparently a special case of Leray spectral sequence. I'll quote the interesting part :

Let $\phi$ be a torsion sheaf on $X$, $f : X \to Y$ a morphism of schemes. Then we have a Leray spectral sequence $E_2^{pq} = H^p_c(Y, R^q f_{!} \phi ) \Rightarrow H^{p+q}_c(X, \phi)$. The way we use this is as follows.

Suppose that all the fibres of $f$ are isomorphic to a fixed scheme $Z$ such that $H^q_c(Z, \phi) = 0$ except for $q= q_0$. Then $H^p_c(Y, R^{q_0} f_{!} \phi ) \simeq H^{p+q}_c(X, \phi)$.

The reference I'm looking for is for the second part of what I have quotequoted.

Since I just happened to work with spectral sequences, maybe this statement is obviously equivalent to the definition of convergence of spectral sequences, in which case I'm sorry for asking.

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# Special case of Leray spectral sequence

I am looking for a reference for what is stated in Srinivasan's book "Representations of Finite Chevalley Groups", which is apparently a special case of Leray spectral sequence. I'll quote the interesting part :

Let $\phi$ be a torsion sheaf on $X$, $f : X \to Y$ a morphism of schemes. Then we have a Leray spectral sequence $E_2^{pq} = H^p_c(Y, R^q f_{!} \phi ) \Rightarrow H^{p+q}_c(X, \phi)$. The way we use this is as follows.

Suppose that all the fibres of $f$ are isomorphic to a fixed scheme $Z$ such that $H^q_c(Z, \phi) = 0$ except for $q= q_0$. Then $H^p_c(Y, R^{q_0} f_{!} \phi ) \simeq H^{p+q}_c(X, \phi)$.

The reference I'm looking for is for the second part of what I have quote.

Since I just happened to work with spectral sequences, maybe this statement is obviously equivalent to the definition of convergence of spectral sequences, in which case I'm sorry for asking.