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Théorème de de Smit et Lenstra, démonstration élémentaire

Henri Lombardi, Claude Quitté

Abstract

We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"

Théorème de de Smit et Lenstra, démonstration élémentaire

Abstract

We give an elementary and constructive proof for a theorem of de Smit et Lenstra. Note: In version 1, was missing the proof that "completely secant" implies "1-secant"

Paper Structure

This paper contains 4 sections, 4 theorems, 5 equations.

Table of Contents

  1. Introduction
  2. Suites régulières, $1$-sécantes, complètement sécantes
  3. Suites $1$-sécantes et platitude
  4. Une platitude remarquable

Key Result

Proposition 5

Toute suite régulière est $1$-sécante.

Theorems & Definitions (4)

  • Proposition 5
  • Proposition 6: extension des scalaires et suite régulière
  • Proposition 7: extension des scalaires et suite $1$-sécante
  • Proposition 10