Let p be a prime. We prove that a positive solution to Efrat's Elementary Type Conjecture implies a positive solution to the strengthened version of Minač-Tân's Massey Vanishing Conjecture in the case of finitely generated maximal pro-p Galois groups whose pro-p cyclotomic character has torsion-free image. Consequently, the maximal pro-p Galois group of a field K containing a root of 1 of order p (and also the square root of -1 if p=2) satisfies the strong n-Massey vanishing property for every n>2 (which is equivalent to the cup-defining n-Massey product property for every n>2, as defined by Minač-Tân) in several relevant cases.

Massey products in Galois cohomology and the Elementary Type Conjecture

claudio quadrelli
2024-01-01

Abstract

Let p be a prime. We prove that a positive solution to Efrat's Elementary Type Conjecture implies a positive solution to the strengthened version of Minač-Tân's Massey Vanishing Conjecture in the case of finitely generated maximal pro-p Galois groups whose pro-p cyclotomic character has torsion-free image. Consequently, the maximal pro-p Galois group of a field K containing a root of 1 of order p (and also the square root of -1 if p=2) satisfies the strong n-Massey vanishing property for every n>2 (which is equivalent to the cup-defining n-Massey product property for every n>2, as defined by Minač-Tân) in several relevant cases.
2024
2024
https://www.sciencedirect.com/science/article/abs/pii/S0022314X23002263
Galois cohomology, Massey products, absolute Galois groups, elementary type conjecture.
Quadrelli, Claudio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2160171
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