Related papers: Generalized Bockstein maps and Massey products

We consider the p-Zassenhaus filtration (G_n) of a profinite group G. Suppose that G=S/N for a free profinite group S and a normal subgroup N of S contained in S_n. Under a cohomological assumption on the n-fold Massey products (which holds…

We consider certain Massey products in the cohomology of a Galois extension of fields with coefficients in p-power roots of unity. We prove formulas for these products both in general and in the special case that the Galois extension in…

A central conjecture of Coates and Sujatha predicts that the fine Selmer group of any $p$-adic Galois representation is cotorsion over the relevant Iwasawa algebra with vanishing $\mu$-invariant, generalizing Iwasawa's original conjecture…

Translating results due to J. Labute into group cohomological language, A. Schmidt proved that a finitely presented pro-p-group G is mild and hence of cohomological dimension cd G=2 if $H^1(G,\F_p)=U\oplus V$ as $\F_p$-vector space and the…

Motivated by the cohomology theory of loop spaces, we consider a special class of higher order homotopy commutative differential graded algebras and construct the filtered Hirsch model for such an algebra $A$. When $x\in H(A)$ with…

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 mod-p Galois cohomology of F, due to Hopkins, Wickelgren, Minac, and Tan, to classical…

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…

Let $p$ be a prime. We characterize the oriented right-angled Artin pro-$p$ groups whose $\mathbb{F}_p$-cohomology algebra yields no essential $n$-fold Massey products for every $n>2$, in terms of the associated digraph. Moreover, we show…

Let pi be a pro-l completion of a free group, and let G be a profinite group acting continuously on pi. First suppose the action is given by a character. Then the boundary maps delta_n: H^1(G, pi/[pi]_n) -> H^2(G, [pi]_n/[pi]_{n+1}) are…

We propose an approach to study non-Abelian Iwasawa theory, using the idea of Johnson homomorphisms in low dimensional topology. We introduce arithmetic analogues of Johnson homomorphisms/maps, called the p-Johnson homomorphisms/maps,…

We compute Iwasawa $\lambda$ invariant in terms of Massey products in Galois cohomology with restricted ramification. When applied to imaginary quadratic fields and cyclotomic fields, we obtain a new proof and generalization of results of…

In this paper, we relate three objects. The first is a particular value of a cup product in the cohomology of the Galois group of the maximal unramified outside p extension of a cyclotomic field containing the pth roots of unity. The second…

The classical deformation theory of Lie algebras involves different kinds of Massey products of cohomology classes. Even the condition of extendibility of an infinitesimal deformation to a formal one-parameter deformation of a Lie algebra…

We show how and when it is possible to detect and recover higher Massey products on the cohomology $H$ of a differential graded algebra $A$ with higher multiplications on quasi-isomorphic $A_\infty$ structures on $H$.

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 any fields. This is the first time when…

We fix a prime p and construct new cases of pro-p extensions of number fields with restricted ramification and splitting, whose Galois groups decompose as coproducts of pro-p absolute Galois groups of local fields. As a consequence, these…

We study the vanishing of four-fold Massey products in mod p Galois cohomology. First, we describe a sufficient condition, which is simply expressed by the vanishing of some cup-products, in direct analogy with the work of Guillot,…

We show that an often used example of a cohomology algebra with non-vanishing triple Massey product is intrinsically A_3-formal and therefore, in fact, cannot be realized as the cohomology of a differential graded algebra with non-vanishing…

In this paper, we develop a new necessary and sufficient condition for the vanishing of 4-Massey products of elements in the mod-2 Galois cohomology of a field. This new description allows us to define a splitting variety for 4-Massey…

The theory of generalized matric Massey products has been applied for some time to $A$-modules $M$, $A$ a $k$-algebra. The main application is to compute the local formal moduli $\hat{H}_M$, isomorphic to the local ring of the moduli of…