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Perfectoid fields in the language of rings

Franziska Jahnke, Ferréol Lavaud

Abstract

Building on work of the first author and Kartas, we identify the elementary class generated by all perfectoid fields of fixed residue characteristic $p$ in the language of rings.

Perfectoid fields in the language of rings

Abstract

Building on work of the first author and Kartas, we identify the elementary class generated by all perfectoid fields of fixed residue characteristic in the language of rings.
Paper Structure (4 sections, 9 theorems, 11 equations)

This paper contains 4 sections, 9 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Notation and nomenclature
  3. Perfectoid fields in the language of valued fields
  4. Perfectoid fields in the language of rings

Key Result

Lemma 2.3

Theorems & Definitions (20)

  • Example 2.1
  • Definition
  • Lemma 2.3
  • Proof
  • Theorem 2.4: JK25
  • Corollary 2.5
  • proof
  • Proposition 3.1
  • Proof
  • Remark 3.2
  • ...and 10 more