Lemma 92.4.4 (08QE)—The Stacks project

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Table of contents
Part 6: Deformation Theory
Chapter 92: The Cotangent Complex
Section 92.4: Simplicial resolutions and derived lower shriek
Lemma 92.4.4 (cite)

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Lemma 92.4.4. If $A \to B$ is a ring map, then $L\pi _!(\pi ^{-1}M) = M$ with $\pi$ as in (92.4.0.1).

Proof. This follows from Lemma 92.4.1 which tells us $L\pi _!(\pi ^{-1}M)$ is computed by $(\pi ^{-1}M)(P_\bullet , \epsilon )$ which is the constant simplicial object on $M$ . $\square$

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