Algebraic Stack

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Algebraic stacks describe families of geometric objects while retaining their automorphisms. Start with the three conditions in the definition and identify the separate roles of descent, the diagonal, and a smooth scheme atlas.

Before opening the references

Scheme · Sheaf · groupoid · Representable Functor

Where to read

  1. Start here: The Stacks Project — Algebraic stacks

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

    Section 94.12, Definition 94.12.1 and the comparison of smooth and étale scheme coverings

    Checked 2026-10-16

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Algebraic Geometry in the library · Preparation and skip guidance

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