We prove that Galois cohomology satisfies several surprisingly strong versions of Koszul properties, under a well known conjecture, in the finitely generated case. In fact, these versions of Koszulity hold for all finitely generated maximal pro-p quotients of absolute Galois groups which are currently understood. We point out several of these unconditional results which follow from our work. We show how these enhanced versions are preserved under certain natural operations on algebras, generalising several results that were previously established only in the commutative case. The subject matter in this paper contains topics which are used in various branches of algebra and computer science.

中文翻译：

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Galois同调学中增强的Koszul性质

我们证明，在有限生成的情况下，在一个众所周知的猜想下，伽罗瓦的同调满足了Koszul性质的几个令人惊讶的强版本。事实上，这些版本Koszulity持有的全部有限生成最大亲p这是目前了解绝对伽罗瓦群的商数。我们指出了我们工作中的一些无条件结果。我们展示了如何在代数上的某些自然运算下保留这些增强的版本，并概括了以前仅在可交换情况下建立的几个结果。本文的主题包含在代数和计算机科学的各个分支中使用的主题。