论文标题
绝对Galois组的算术ORR不变性
Arithmetic Orr invariants of absolute Galois groups
论文作者
论文摘要
基于映射课程组和绝对Galois组之间的类比，我们引入了算术pro-$ \ ell $ ORR不变性的类似物，用于与GALOIS在of tale的基本组基本组相关的Galois元素。同时，我们还引入了Pro-$ \ ell $ orr空间作为ORR空间的算术类似物，其第三个同型组是ORR不变的目标组。然后，我们将其等级确定为$ \ mathbb {z} _ {\ ell} $ - 遵循Igusa-orr的计算的模块。此外，我们研究了与埃伦伯格（Ellenberg）的障碍物与$π_1$ sections的关系，在Grothendieck的部分猜想的背景下，与下中央系列过滤相关。
Based on the analogies between mapping class groups and absolute Galois groups, we introduce an arithmetic pro-$\ell$ 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-$\ell$ 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 $\mathbb{Z}_{\ell}$-module following Igusa-Orr's computation. Moreover, we investigate its relation with Ellenberg's obstruction to $π_1$-sections associated with lower central series filtration in the context of Grothendieck's section conjecture.
