Definition 92.3.2 (08PN)—The Stacks project

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Table of contents
Part 6: Deformation Theory
Chapter 92: The Cotangent Complex
Section 92.3: The cotangent complex of a ring map
Definition 92.3.2 (cite)

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Definition 92.3.2. The cotangent complex $L_{B/A}$ of a ring map $A \to B$ is the complex of $B$ -modules associated to the simplicial $B$ -module

$\Omega _{P_\bullet /A} \otimes _{P_\bullet , \epsilon } B$

where $\epsilon : P_\bullet \to B$ is the standard resolution of $B$ over $A$ .

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