Arithmetic Orr invariants of absolute Galois groups
| Autor: | Kodani, Hisatoshi, Terashima, Yuji |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 65 pages; table of contents is inserted; several minor errors are corrected; minor modifications in p.26, p.29, p.56; to appear in Int. Math. Res. Not. IMRN |
| Databáze: | arXiv |
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