Crystalline Cohomology

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Crystalline cohomology uses divided-power thickenings to study geometry in characteristic p. Begin by identifying the objects of the crystalline site, then follow the affine reduction that turns its cohomology into an algebraic problem.

Before opening the references

Scheme · Sheaf · Ideal of a Commutative Ring · Chain Complex of Modules

Where to read

  1. Start here: The Stacks Project — The crystalline site

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

    Section 60.9, Definition 60.9.1 and Lemma 60.9.2

    Checked 2026-10-16

  2. Reference: The Stacks Project — General remarks on cohomology

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

    Section 60.18, Lemmas 60.18.1–60.18.2

    Checked 2026-10-16

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