23 problems

Mináč–Tân's conjecture. For every field $F$, every prime $p$, and every positive integer $n$, $G_F$ satisfies $n$-Massey vanishing with respect to $p$.

Buchstaber's conjecture. The algebra $H^*(W^+)$ is generated, using some non-trivial Massey products, by its first cohomology $H^1(W^+)$.

Let the Bendersky–Gitler spectral sequence be the spectral sequence associated with the nerve of the covering of the fat diagonal in $M^k$, with higher differentials…

Let $p$ be a prime number and $n\geq 3$ an integer. Let $F$ be a field, which contains a primitive $p$-th root of unity if $\operatorname{char}(F)\not=p$. Let $G_F$ denote the abso…

Let $K=\mathbf{Q}(\mu_p)$ with $p$ odd, let $K_\infty=\mathbf{Q}(\mu_{p^\infty})$, and let $L_\infty/K_\infty$ be a ${\mathbf Z}_p$-extension defined by a sequence of cyclotomic…

Let $\Gamma$ be a group. For each $k$, let $c_k(\Gamma)$ denote the largest cardinality of a primitive set in $H^1(\Gamma,\mathbb Z)$ for which all $k$-fold Massey products vanish.…

Minac--Tan's conjecture. For every field $F$ and prime $p$, $G_F$ satisfies $n$-Massey vanishing with respect to $p$.

Group-theoretic Frattini-resistance conjecture. If there exist homomorphisms of pro-$p$ groups $\tau,\tau':G\to\mathbb{U}_3$ such that

Frattini-resistance conjecture. If $G$ is Frattini-resistant, then there are no essential triple Massey products in the $\mathbb{Z}/p$-cohomology of $G$.

Let $p$ be a prime, let $\mathbb{K}$ be a field containing a root of unity of order $p$, and let $G_{\mathbb{K}}(p)$ be its maximal pro-$p$ Galois group. Write … For $p=2$, Hopkins…

Nagy–Nordström's conjecture. The rational homotopy type of $M$ is determined by its pentagon Massey tensor.

Let $p$ be a prime, let $G$ be a maximal pro-$p$ Galois group, and let $n\geq 3$. A group has the $n$-vanishing Massey product property if every homomorphism…

Let $F$ be a field, let $p$ be a prime, and let $n\geq 3$. For $\chi_1,\dots,\chi_n\in H^1(\Gamma_F,\mathbb Z/p\mathbb Z)$, the Massey product…

Let $F$ be a field, let $p$ be a prime, let $n\geq 3$, and let $\chi_1,\dots,\chi_n\in H^1(F,\mathbb Z/p\mathbb Z)$. The Massey product…

Let $p>3$ be a prime, and let $K$ be an imaginary quadratic field whose class group has $p$-rank two. Set … Choose a basis $x,y$ of $H^1(G,\mathbb{Z}/p\mathbb{Z})$, and let…

Let $X$ and $Y$ be closed $(n{-}1)$-connected $m$-manifolds, with $n>1$ and $m\leq 5n-2$. Let … be an isomorphism of cohomology algebras. Write $\mathcal{T}_b$ and $\mathcal{T}_c$…

Let $X$ and $Y$ be closed $(n{-}1)$-connected manifolds of dimension at most $5n-2$, and suppose their Bianchi–Massey tensors are trivial. Let … be an isomorphism of cohomology alg…

Massey obstruction conjecture. These cohomology classes are obstructions to lifting $\widetilde f_4$ to a map

Minac and T^an's conjecture. Every defined $m$-fold Massey product on $H^1(G_{\mathbb{K}}(p),\mathbb{F}_p)$ vanishes, for every $m\geq 3$.

Let $k$ be a field, let $p$ be a prime, and let $n\geq 3$. For cohomology classes … consider the $n$-fold Massey product…

Let $F$ be a field, let $\Gamma=\operatorname{Gal}(\overline{F}/F)$ be its absolute Galois group, let $p$ be a prime, and let…

Let $F$ be a field containing a primitive $l$-th root of unity, and let $G_F$ be its absolute Galois group. Consider tuple Massey products of degree-one elements in the cohomology…

Let $F$ be a field, let $F_s$ be a separable closure, and let $G_F={\rm Gal}(F_s/F)$ be its absolute Galois group. Let $p$ be a prime number and $n\geq 3$ an integer. The vanishing…