p-adic Analysis

p-adic numbers, analysis over Q_p, and rigid geometry.

foundation tier

p-adic Analysis. p-adic numbers, analysis over Q_p, and rigid geometry.

Foundations and canonical references

The standard treatments of p-adic analysis approach the subject from complementary angles. Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions (1984) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.

Open methodological questions for p-adic analysis include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 1984
    p-adic Numbers, p-adic Analysis, and Zeta-Functions
    koblitz-1984

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  1. 01

    Perfectoid Spaces

    Scholze's perfectoid spaces and the tilting equivalence.
  2. 02

    p-adic Hodge Theory

    Fontaine's theory, prismatic cohomology, and crystalline representations.

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