$A_3$-形式性对于pro-2 Demushkin群
$A_3$-formality for pro-2 Demushkin groups
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中文总结 AI 辅助
研究微分分次代数的弱形式性——$A_3$-形式性，通过计算Benson-Krause-Schwede典范类，证明所有pro-2 Demushkin群的连续上链的微分分次$\mathbb{F}_2$-代数是$A_3$-形式的。
中文摘要 AI 辅助
我们研究微分分次代数的一种弱形式性，称为$A_3$-形式性，并证明所有pro-$2$ Demushkin群的连续上链的微分分次$\mathbb{F}_2$-代数是$A_3$-形式的。我们通过利用Demushkin、Serre和Labute对pro-$2$ Demushkin群的分类，显式计算Benson--Krause--Schwede典范类来证明这一结果。与奇素数情形相比，新思路是将典范类的数据解释为定义更高Massey积的系统。
英文摘要
We study a weak form of formality for differential graded algebras, called $A_3$-formality, and show that the differential graded $\mathbb{F}_2$-algebras of continuous cochains of all pro-$2$ Demushkin groups are $A_3$-formal. We prove this result by an explicit computation of the Benson--Krause--Schwede canonical class using the classification of pro-$2$ Demushkin groups by Demushkin, Serre, and Labute. Compared to the case of odd primes, the new idea is to interpret the data of the canonical class as defining systems of higher Massey products.
