论文标题
GALOIS共同学和基本类型的猜想中的Massey产品
Massey products in Galois cohomology and the Elementary Type Conjecture
论文作者
论文摘要
令$ p $为素数。我们证明，对EFRAT基本类型的猜想的积极解决方案意味着在有限生成的最大值Pro-P $ Galois群体的情况下，Minač--Tân的Massey Vanishing猜想的积极解决方案，其Pro-P $ P $ Cyclotomic cyclotomic cartomic contormion conture torsion torsion free torsion free图像。因此，如果$ p $ $ p $的1个根（以及\ sqrt {-1}）如果$ n $ n $ n $ n $ n $ -n $ -n $ - 每一个$ n $ n propport up n $ n propport ups $ n，则最大的$ p $ p $ p $ p $ galois组包含1个订单$ p $ 1的根（以及\ sqrt {-1}的根）。 Minač--tân）在几种相关情况下。
Let $p$ be a prime. We prove that a positive solution to Efrat's Elementary Type Conjecture implies a positive solution to the strengthened version of Minač--Tân's Massey Vanishing Conjecture in the case of finitely generated maximal pro-$p$ Galois groups whose pro-$p$ cyclotomic character has torsion-free image. Consequently, the maximal pro-$p$ Galois group of a field $\mathbb{K}$ containing a root of 1 of order $p$ (and also \sqrt{-1} if $p=2$) satisfies the strong $n$-Massey vanishing property for every $n>2$ (which is equivalent to the cup-defining $n$-Massey product property for every $n>2$, as defined by Minač--Tân) in several relevant cases.
