Lemma 37.13.14 (0FV5)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 37: More on Morphisms
Section 37.13: The naive cotangent complex
Lemma 37.13.14 (cite)

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Lemma 37.13.14. Consider a cartesian diagram of schemes

$\xymatrix{ X' \ar[r]_{g'} \ar[d] & X \ar[d] \\ Y' \ar[r] & Y }$

The canonical map $(g')^*\mathop{N\! L}\nolimits _{X/Y} \to \mathop{N\! L}\nolimits _{X'/Y'}$ induces an isomorphism on $H^0$ and a surjection on $H^{-1}$ .

Proof. Translated into algebra this is More on Algebra, Lemma 15.85.2. To do the translation use Lemma 37.13.2. $\square$

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