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Research Article

Massey products in Galois cohomology and Pythagorean fields

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Received 13 Dec 2023, Accepted 26 Feb 2024, Published online: 06 May 2024
 

Abstract

We prove that a strengthened version of Minač–Tân’s Massey Vanishing Conjecture holds true for fields with a finite number of square classes whose maximal pro-2 Galois group is of elementary type (as defined by I. Efrat). In particular, this proves Minač–Tân’s Massey Vanishing Conjecture for Pythagorean fields with a finite number of square classes and their finite extensions.

2020 MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgments

The author wishes to thank I. Efrat, E. Matzri, J. Minač, F.W. Pasini, and N.D. Tân, for several inspiring discussions on Massey products in Galois cohomology and pro-p groups of elementary type, which occurred in the past years; and the anonymous referee for the helpful comments.

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