Triple Massey products of weight (1,n,1) in Galois cohomology

Eliyahu Matzri

doi:10.1016/j.jalgebra.2017.11.036

Triple Massey products of weight (1,n,1) in Galois cohomology

Eliyahu Matzri

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Fix an arbitrary prime p. Let F be a field containing a primitive p-th root of unity, with absolute Galois group G_F, and let Hⁿ denote its mod p cohomology group Hⁿ(G_F,Z/pZ). The triple Massey product (abbreviated 3MP) of weight (n,k,m)∈N³ is a partially defined, multi-valued function 〈⋅,⋅,⋅〉:Hⁿ×H^k×H^m→H^n+k+m−1. In this work we prove that for an odd prime p, any defined 3MP of weight (1,k,1) contains zero.

Original language	English
Pages (from-to)	272-280
Number of pages	9
Journal	Journal of Algebra
Volume	499
DOIs	https://doi.org/10.1016/j.jalgebra.2017.11.036
State	Published - 1 Apr 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Funding

The author would like to thank I. Efrat for many interesting discussions and helpful suggestions, in particular for encouraging him to add the last part of the work avoiding the use of Kraines [6]. The author would also like to thank the anonymous referee for many interesting comments and suggestions. This research was supported by the Israel Science Foundation (grant No. 630/17).

Funders	Funder number
Israel Science Foundation	630/17

Keywords

External cohomological operations
Galois cohomology
Massey products

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10.1016/j.jalgebra.2017.11.036

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abstract = "Fix an arbitrary prime p. Let F be a field containing a primitive p-th root of unity, with absolute Galois group GF, and let Hn denote its mod p cohomology group Hn(GF,Z/pZ). The triple Massey product (abbreviated 3MP) of weight (n,k,m)∈N3 is a partially defined, multi-valued function 〈⋅,⋅,⋅〉:Hn×Hk×Hm→Hn+k+m−1. In this work we prove that for an odd prime p, any defined 3MP of weight (1,k,1) contains zero.",

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N2 - Fix an arbitrary prime p. Let F be a field containing a primitive p-th root of unity, with absolute Galois group GF, and let Hn denote its mod p cohomology group Hn(GF,Z/pZ). The triple Massey product (abbreviated 3MP) of weight (n,k,m)∈N3 is a partially defined, multi-valued function 〈⋅,⋅,⋅〉:Hn×Hk×Hm→Hn+k+m−1. In this work we prove that for an odd prime p, any defined 3MP of weight (1,k,1) contains zero.

AB - Fix an arbitrary prime p. Let F be a field containing a primitive p-th root of unity, with absolute Galois group GF, and let Hn denote its mod p cohomology group Hn(GF,Z/pZ). The triple Massey product (abbreviated 3MP) of weight (n,k,m)∈N3 is a partially defined, multi-valued function 〈⋅,⋅,⋅〉:Hn×Hk×Hm→Hn+k+m−1. In this work we prove that for an odd prime p, any defined 3MP of weight (1,k,1) contains zero.

KW - External cohomological operations

KW - Galois cohomology

KW - Massey products

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JO - Journal of Algebra

JF - Journal of Algebra

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Triple Massey products of weight (1,n,1) in Galois cohomology

Abstract

Bibliographical note

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Keywords

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