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On the behavior of Massey products under field extension

Aleksandar Milivojevic

Abstract

We show that global vanishing of Massey products on a commutative differential graded algebra is not invariant under field extension. Non-vanishing triple Massey products remain non-vanishing upon field extension, while higher Massey products can generally vanish. If the field being extended is algebraically closed, all non-vanishing Massey products remain non-vanishing on a finite type commutative differential graded algebra.

On the behavior of Massey products under field extension

Abstract

We show that global vanishing of Massey products on a commutative differential graded algebra is not invariant under field extension. Non-vanishing triple Massey products remain non-vanishing upon field extension, while higher Massey products can generally vanish. If the field being extended is algebraically closed, all non-vanishing Massey products remain non-vanishing on a finite type commutative differential graded algebra.
Paper Structure (6 sections, 7 theorems, 31 equations)

This paper contains 6 sections, 7 theorems, 31 equations.

Table of Contents

  1. Introduction
  2. Global vanishing of Massey products is not preserved under field extension
  3. Behavior of individual Massey products under field extension
  4. Triple Massey products persist under field extension
  5. Non-trivial quadruple Massey products can become trivial upon field extension
  6. Extending from an algebraically closed field

Key Result

Theorem 1.1

We have the following:

Theorems & Definitions (15)

  • Theorem 1.1
  • Lemma 2.1
  • proof
  • Corollary 2.2
  • proof
  • Remark 2.3
  • Corollary 2.4
  • proof
  • Proposition 2.5
  • Remark 2.6
  • ...and 5 more