Massey products in Galois cohomology and the Elementary Type Conjecture
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916117906194432 |
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| author | Quadrelli, Claudio |
| author_facet | Quadrelli, Claudio |
| contents | 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 $\mathbb{K}$ containing a root of 1 of order $p$ (and also \sqrt{-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_16232 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Massey products in Galois cohomology and the Elementary Type Conjecture Quadrelli, Claudio Number Theory Primary 12G05, Secondary 20E18, 20J06, 12F10 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 $\mathbb{K}$ containing a root of 1 of order $p$ (and also \sqrt{-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. |
| title | Massey products in Galois cohomology and the Elementary Type Conjecture |
| topic | Number Theory Primary 12G05, Secondary 20E18, 20J06, 12F10 |
| url | https://arxiv.org/abs/2203.16232 |