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<p>We show that a strong vanishing conjecture for <i>n</i>-fold Massey products holds for fields of virtual cohomological dimension at most 1 using a theorem of Haran. We also prove the same for PpC fields, using results of Haran–Jarden. Finally we give a purely group-theoretical construction of a pro-2 group which satisfies the weak Massey vanishing property for every <i>n</i> ≥ 3, but does not satisfy the strong Massey vanishing property for <i>n</i> = 4.</p>

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The strong Massey vanishing conjecture for fields with virtual cohomological dimension at most 1

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月4日

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  • Ambrus Pál,
  • Endre Szabó

摘要

We show that a strong vanishing conjecture for n-fold Massey products holds for fields of virtual cohomological dimension at most 1 using a theorem of Haran. We also prove the same for PpC fields, using results of Haran–Jarden. Finally we give a purely group-theoretical construction of a pro-2 group which satisfies the weak Massey vanishing property for every n ≥ 3, but does not satisfy the strong Massey vanishing property for n = 4.