Arithmetic Orr Invariants of Absolute Galois Groups
Arithmetic Orr Invariants of Absolute Galois Groups
复制标题
绝对伽罗瓦群的算术 Orr 不变量
DOI：
10.1093/imrn/rnac138
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发表时间：
2022
影响因子：
1
通讯作者：
Terashima Yuji
中科院分区：
文献类型：
--
作者：
Kodani Hisatoshi;Terashima Yuji
基于映射类群和绝对伽罗瓦群之间的类比，我们引入了与刺穿射影线的étale基本群上的伽罗瓦作用相关的伽罗瓦元素的奥尔不变量的算术亲类比。同时，我们还引入了pro-Orr空间作为Orr空间的算术模拟，其第三个同伦群是Orr不变量的目标群。然后我们根据 Igusa-Orr 的计算确定其作为模块的排名。此外，我们在格洛腾迪克截面猜想的背景下研究了它与埃伦伯格对与较低中央级数过滤相关的截面的阻碍的关系。
Based on the analogies between mapping class groups and absolute Galois groups, we introduce an arithmetic pro-analogue of Orr invariants for a Galois element associated with Galois action on étale fundamental groups of punctured projective lines. At the same time, we also introduce pro-Orr space as an arithmetic analogue of Orr space whose third homotopy group is a target group of Orr invariant. We then determine its rank as-module following Igusa–Orr’s computation. Moreover, we investigate its relation with Ellenberg’s obstruction to-sections associated with lower central series filtration in the context of Grothendieck’s section conjecture.