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arXiv · 2012.08500

Arithmetic Orr invariants of absolute Galois groups

Hisatoshi Kodani·Yuji Terashima
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Abstract

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 \'etale 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 $\pi_1$-sections associated with lower central series filtration in the context of Grothendieck's section conjecture.

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Hisatoshi Kodani, Yuji Terashima. 2020-12-15. Arithmetic Orr invariants of absolute Galois groups. https://arxiv.org/abs/2012.08500

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