Étale Cohomology

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External reading guide · Graduate

Étale cohomology applies sheaf cohomology to coverings by étale morphisms, providing invariants suited to algebraic geometry over general fields. Begin with the topology and its sheaf condition, then use Mayer–Vietoris as a first structural calculation.

Before opening the references

Scheme · Sheaf · Chain Complex of Modules · Short Exact Sequence of Modules

Where to read

  1. Start here: The Stacks Project — The étale topology

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

    Section 59.4, Definition 59.4.1, the sheaf equalizer condition, and the closing cohomology discussion

    Checked 2026-10-16

  2. Reference: The Stacks Project — Étale cohomology

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

    Section 59.50, Lemma 59.50.1 (Mayer–Vietoris for étale cohomology)

    Checked 2026-10-16

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Algebraic Geometry in the library · Preparation and skip guidance

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