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

Eliyahu Matzri

doi:https://doi.org/10.1016/j.jalgebra.2017.11.036

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

Eliyahu Matzri

Department of Mathematics

Bar-Ilan University

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

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

Keywords

External cohomological operations
Galois cohomology
Massey products

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.1016/j.jalgebra.2017.11.036

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

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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doi = "https://doi.org/10.1016/j.jalgebra.2017.11.036",

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T1 - Triple Massey products of weight (1,n,1) in Galois cohomology

AU - Matzri, Eliyahu

PY - 2018/4/1

Y1 - 2018/4/1

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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U2 - https://doi.org/10.1016/j.jalgebra.2017.11.036

DO - https://doi.org/10.1016/j.jalgebra.2017.11.036

M3 - مقالة

SN - 0021-8693

VL - 499

SP - 272

EP - 280

JO - Journal of Algebra

JF - Journal of Algebra

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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