Perfectoid Space

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Perfectoid spaces glue affinoid charts built from perfectoid algebras. Start with their local definition and use the preceding affinoid results to understand why these charts support a sheaf.

Before opening the references

Scheme · Sheaf · p-adic number field · Commutative Ring

Where to read

  1. Start here: Perfectoid Spaces

    Peter Scholze · Research paper · English · Free full text

    Section 6, Theorem 6.3 and Definition 6.15, printed pp. 30 and 38

    Checked 2026-10-16

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Algebraic Geometry in the library · Preparation and skip guidance

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