Higher Triple Massey products and symbols

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Abstract

Fix an arbitrary prime p. Let F be a field containing a primitive p-th root of unity, with absolute Galois group G F , and let H n denote its mod p cohomology group H n (G F ,Z/pZ). The triple Massey product of weight (n,k,m)∈N 3 is a partially defined, multi-valued function 〈⋅,⋅,⋅〉:H n ×H k ×H m →H n+k+m−1 . In this work we prove that for an arbitrary prime p, any defined 3MP of weight (n,1,m), where the first and third entries are symbols, contains zero; and that any defined 3MP of weight (1,k,1), where the middle entry is a symbol, contains zero.

Original languageEnglish
Pages (from-to)136-146
Number of pages11
JournalJournal of Algebra
Volume527
DOIs
StatePublished - 1 Jun 2019

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

  • External cohomological operations
  • Galois cohomology
  • Massey products
  • Symbols

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