论文标题
在任意领域上退化四倍的梅西产品
Degenerate fourfold Massey products over arbitrary fields
论文作者
论文摘要
我们证明，对于所有字段$ f $的特征，不同于$ 2 $，所有$ a，b，c \ in f^\ times $，mod $ 2 $ 2 $ massey product $ \ langle a，b，c，a \ rangle $一旦定义就消失了。 For every field $F_0$, we construct a field $F$ containing $F_0$ and $a,b,c,d\in F^\times$ such that $\langle a,b,c \rangle$ and $\langle b,c,d \rangle$ vanish but $\langle a,b,c,d \rangle$ is not defined.结果，我们通过构建包含所有统一根源的领域的第一个示例来回答一个问题，并使绝对Galois集团的Mod 2 $ Cochain DGA并不正式。
We prove that, for all fields $F$ of characteristic different from $2$ and all $a,b,c\in F^\times$, the mod $2$ Massey product $\langle a,b,c,a \rangle$ vanishes as soon as it is defined. For every field $F_0$, we construct a field $F$ containing $F_0$ and $a,b,c,d\in F^\times$ such that $\langle a,b,c \rangle$ and $\langle b,c,d \rangle$ vanish but $\langle a,b,c,d \rangle$ is not defined. As a consequence, we answer a question of Positselski by constructing the first examples of fields containing all roots of unity and such that the mod $2$ cochain DGA of the absolute Galois group is not formal.
