亲$p$群体与很少的关系和普遍的Koszulity

arXiv: Group Theory Pub Date : 2020-03-20 DOI:10.7146/MATH.SCAND.A-123644

C. Quadrelli

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引用次数: 5

摘要

设p是素数。我们证明了如果一个最多有2个定义关系的亲$p$群具有二次$\mathbb{F}_p$-上同调，那么这样的代数是普遍的Koszul。这证明了J. Minac等人在具有最多2个定义关系的极大的pro-$p$ Galois群的情况下提出的“普世性Koszulity猜想”。

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Pro-$p$ groups with few relations and universal Koszulity

Let $p$ be a prime. We show that if a pro-$p$ group with at most 2 defining relations has quadratic $\mathbb{F}_p$-cohomology, then such algebra is universally Koszul. This proves the "Universal Koszulity Conjecture" formulated by J. Minac et al. in the case of maximal pro-$p$ Galois groups of fields with at most 2 defining relations.

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arXiv: Group Theory

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