91 The Cotangent Complex
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Section 91.1: Introduction
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Section 91.2: Advice for the reader
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Section 91.3: The cotangent complex of a ring map
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Section 91.4: Simplicial resolutions and derived lower shriek
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Section 91.5: Constructing a resolution
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Section 91.6: Functoriality
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Section 91.7: The fundamental triangle
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Section 91.8: Localization and étale ring maps
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Section 91.9: Smooth ring maps
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Section 91.10: Positive characteristic
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Section 91.11: Comparison with the naive cotangent complex
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Section 91.12: A spectral sequence of Quillen
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Section 91.13: Comparison with Lichtenbaum-Schlessinger
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Section 91.14: The cotangent complex of a local complete intersection
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Section 91.15: Tensor products and the cotangent complex
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Section 91.16: Deformations of ring maps and the cotangent complex
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Section 91.17: The Atiyah class of a module
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Section 91.18: The cotangent complex
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Section 91.19: The Atiyah class of a sheaf of modules
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Section 91.20: The cotangent complex of a morphism of ringed spaces
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Section 91.21: Deformations of ringed spaces and the cotangent complex
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Section 91.22: The cotangent complex of a morphism of ringed topoi
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Section 91.23: Deformations of ringed topoi and the cotangent complex
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Section 91.24: The cotangent complex of a morphism of schemes
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Section 91.25: The cotangent complex of a scheme over a ring
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Section 91.26: The cotangent complex of a morphism of algebraic spaces
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Section 91.27: The cotangent complex of an algebraic space over a ring
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Section 91.28: Fibre products of algebraic spaces and the cotangent complex