\begin{equation*}
\DeclareMathOperator\Coim{Coim}
\DeclareMathOperator\Coker{Coker}
\DeclareMathOperator\Ext{Ext}
\DeclareMathOperator\Hom{Hom}
\DeclareMathOperator\Im{Im}
\DeclareMathOperator\Ker{Ker}
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\newcommand\Cohstack{\mathcal{C}\!\mathit{oh}}
\newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}}
\newcommand\Quotfunctor{\mathrm{Quot}}
\newcommand\Hilbfunctor{\mathrm{Hilb}}
\newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}}
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\newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}}
\newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits}
\newcommand\Picardstack{\mathcal{P}\!\mathit{ic}}
\newcommand\Picardfunctor{\mathrm{Pic}}
\newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}}
\end{equation*}
84 The Cotangent Complex
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Section 84.1: Introduction
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Section 84.2: Advice for the reader
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Section 84.3: The cotangent complex of a ring map
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Section 84.4: Simplicial resolutions and derived lower shriek
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Section 84.5: Constructing a resolution
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Section 84.6: Functoriality
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Section 84.7: The fundamental triangle
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Section 84.8: Localization and étale ring maps
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Section 84.9: Smooth ring maps
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Section 84.10: Comparison with the naive cotangent complex
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Section 84.11: A spectral sequence of Quillen
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Section 84.12: Comparison with Lichtenbaum-Schlessinger
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Section 84.13: The cotangent complex of a local complete intersection
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Section 84.14: Tensor products and the cotangent complex
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Section 84.15: Deformations of ring maps and the cotangent complex
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Section 84.16: The Atiyah class of a module
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Section 84.17: The cotangent complex
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Section 84.18: The Atiyah class of a sheaf of modules
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Section 84.19: The cotangent complex of a morphism of ringed spaces
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Section 84.20: Deformations of ringed spaces and the cotangent complex
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Section 84.21: The cotangent complex of a morphism of ringed topoi
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Section 84.22: Deformations of ringed topoi and the cotangent complex
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Section 84.23: The cotangent complex of a morphism of schemes
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Section 84.24: The cotangent complex of a scheme over a ring
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Section 84.25: The cotangent complex of a morphism of algebraic spaces
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Section 84.26: The cotangent complex of an algebraic space over a ring
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Section 84.27: Fibre products of algebraic spaces and the cotangent complex