Lemma 92.5.3. Let A be a Noetherian ring. Let A \to B be a finite type ring map. Let \pi , \underline{B} be as in (92.4.0.1). If \mathcal{F} is an \underline{B}-module such that \mathcal{F}(P, \alpha ) is a finite B-module for all \alpha : P = A[x_1, \ldots , x_ n] \to B, then the cohomology modules of L\pi _!(\mathcal{F}) are finite B-modules.
Proof. By Lemma 92.4.1 and Proposition 92.5.2 we can compute L\pi _!(\mathcal{F}) by a complex constructed out of the values of \mathcal{F} on finite type polynomial algebras. \square
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