The Massey vanishing conjecture for number fields

Yonatan Harpaz; Olivier Wittenberg

doi:10.1215/00127094-2022-0004

Abstract

A conjecture of Mináč and Tân predicts that for any $n\ge 3$ , any prime p, and any field k, the Massey product of n Galois cohomology classes in ${H^{1}}(k,\mathbf{Z}/ p\mathbf{Z})$ must vanish if it is defined. We establish this conjecture when k is a number field.

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Yonatan Harpaz. Olivier Wittenberg. "The Massey vanishing conjecture for number fields." Duke Math. J. 172 (1) 1 - 41, 15 January 2023. https://doi.org/10.1215/00127094-2022-0004

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Received: 15 April 2019; Revised: 15 December 2021; Published: 15 January 2023

First available in Project Euclid: 6 December 2022

zbMATH: 07653250

MathSciNet: MR4533716

Digital Object Identifier: 10.1215/00127094-2022-0004

Subjects:

Primary: 11R34 , 55S30

Secondary: 14G05 , 14M17

Keywords: Galois cohomology , higher Massey products , Massey vanishing conjecture , number fields

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