Cotangent Complex

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The cotangent complex extends the module of differentials by retaining homological information from a resolution. Start with a ring map and its polynomial resolution, then read how the construction localizes on affine charts of a scheme morphism.

Before opening the references

Scheme · Chain Complex of Modules · Tensor Product of Modules · Ext Group of Modules

Where to read

  1. Start here: The Stacks Project — The cotangent complex of a ring map

    The Stacks Project Authors · Online reference · English · Free full text

    Section 92.3, Definitions 92.3.1–92.3.2

    Checked 2026-10-16

  2. Reference: The Stacks Project — The cotangent complex of a morphism of schemes

    The Stacks Project Authors · Online reference · English · Free full text

    Section 92.24, Definition 92.24.1 and Lemma 92.24.2

    Checked 2026-10-16

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