• Corpus ID: 119658056

Triple Massey products in Galois cohomology

@article{Matzri2014TripleMP,
  title={Triple Massey products in Galois cohomology},
  author={Eliyahu Matzri},
  journal={arXiv: Rings and Algebras},
  year={2014}
}
  • Eliyahu Matzri
  • Published 15 November 2014
  • Mathematics
  • arXiv: Rings and Algebras
Fix an arbitrary prime $p$. Let $F$ be a field, containing a primitive $p$-th root of unity, with absolute Galois group $G_F$. The triple Massey product (in the mod-$p$ Galois cohomology) is a partially defined, multi-valued function $\langle \cdot,\cdot,\cdot \rangle: H^1(G_F)^3\rightarrow H^2(G_F).$ In this work we prove a conjecture made in [11] stating that any defined triple Massey product contains zero. As a result the pro-$p$ groups appearing in [11] are excluded from being absolute… 
Triple Massey Products with weight in Galois cohomology
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 $H^n$ denote its mod $p$ cohomology group
Triple Massey products and absolute Galois groups
Let $p$ be a prime number, $F$ a field containing a root of unity of order $p$, and $G_F$ the absolute Galois group. Extending results of Hopkins, Wickelgren, Minac and Tan, we prove that the triple
3-fold Massey products in Galois cohomology -- The non-prime case
For $m\geq2$, let $F$ be a field of characteristic prime to $m$ and containing the roots of unity of order $m$, and let $G_F$ be its absolute Galois group. We show that the 3-fold Massey products
Four-fold Massey products in Galois cohomology
In this paper, we develop a new necessary and sufficient condition for the vanishing of $4$ -Massey products of elements in the modulo- $2$ Galois cohomology of a field. This new description allows
Triple Massey products over global fields
Let $K$ be a global field which contains a primitive $p$-th root of unity, where $p$ is a prime number. M. J. Hopkins and K. G. Wickelgren showed that for $p=2$, any triple Massey product over $K$
Counting Galois ${\mathbb U}_4({\mathbb F}_p)$-extensions using Massey products
We use Massey products and their relations to unipotent representations to parametrize and find an explicit formula for the number of Galois extensions of a given local field with the prescribed
Relations in the maximal pro-𝑝 quotients of absolute Galois groups
We observe that some fundamental constructions in Galois theory can be used to obtain interesting restrictions on the structure of Galois groups of maximal p p -extensions of fields
...
...

References

SHOWING 1-10 OF 17 REFERENCES
Triple Massey products and Galois theory
We show that any triple Massey product with respect to prime 2 contains 0 whenever it is defined over any field. This extends the theorem of M. J. Hopkins and K. G. Wickelgren, from global fields to
Triple Massey products over global fields
Let $K$ be a global field which contains a primitive $p$-th root of unity, where $p$ is a prime number. M. J. Hopkins and K. G. Wickelgren showed that for $p=2$, any triple Massey product over $K$
Vanishing of Massey Products and Brauer Groups
Abstract Let $p$ be a prime number and $F$ a field containing a root of unity of order $p$ . We relate recent results on vanishing of triple Massey products in the $\bmod-p $ Galois cohomology of $F$
Degeneracy and decomposability in abelian crossed products
MASSEY HIGHER PRODUCTS
In this paper, we shall investigate some properties of a class of higher order cohomology operations of several variables. These operations, the higher products, were defined by Massey as a
Cohomology of number fields
Part I Algebraic Theory: Cohomology of Profinite Groups.- Some Homological Algebra.- Duality Properties of Profinite Groups.- Free Products of Profinite Groups.- Iwasawa Modules.- Part II Arithmetic
...
...