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Inertia of retracts in Demushkin groups

Henrique Souza

Abstract

Exploring inequalities regarding the rank and relation gradients of pro-p modules and building upon recent results of Y. Antolín, A. Jaikin-Zapiran and M. Shusterman, we prove that every retract of a Demushkin group is inert in the sense of the Dicks-Ventura Inertia Conjecture.

Inertia of retracts in Demushkin groups

Abstract

Exploring inequalities regarding the rank and relation gradients of pro-p modules and building upon recent results of Y. Antolín, A. Jaikin-Zapiran and M. Shusterman, we prove that every retract of a Demushkin group is inert in the sense of the Dicks-Ventura Inertia Conjecture.

Paper Structure

This paper contains 3 sections, 6 theorems, 31 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Inertia of retracts

Key Result

Theorem 1.1

Every retract of a Demushkin group is inert.

Theorems & Definitions (11)

  • Theorem 1.1
  • Definition 2.1
  • Proposition 2.2: jaikin_shusterman_19
  • Lemma 2.3: jaikin_shusterman_19
  • Lemma 3.1
  • proof
  • Proposition 3.2
  • proof
  • Theorem 3.3
  • proof
  • ...and 1 more