Perfectoid Field

← Encyclopedia

External reading guide · Research

Perfectoid fields provide the valued-field setting for tilting. Read the completeness, nondiscreteness, and Frobenius conditions together, then follow the inverse-limit construction of the tilt.

Before opening the references

field · p-adic number field · p-adic additive valuation · Categorical Limit

Where to read

  1. Start here: Perfectoid Spaces

    Peter Scholze · Research paper · English · Free full text

    Section 3, Definition 3.1 and Lemma 3.4, printed pp. 15–16

    Checked 2026-10-16

Continue from here

Algebraic Geometry in the library · Preparation and skip guidance

Suggest an edit · Report a correction

Original orientation: CC BY-SA 4.0. Linked texts retain their own licences.