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On the existence of non-geometric sections of arithmetic fundamental groups

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Abstract

We show the existence of group-theoretic sections of the “étale-by-geometrically abelian” quotient of the arithmetic fundamental group of hyperbolic curves over \(p\)-adic local fields relative to a proper and flat model which are non-geometric, i.e., which do not arise from rational points.

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Acknowledgments

I would like very much to thank Akio Tamagawa for several discussions we had on the topic of this paper. I also thank the referee for his/her valuable comments.

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  1. College of Engineering, Mathematics, and Physical Sciences, University of Exeter, Harrison Building, North Park Road, Exeter, EX4 4QF, UK

    Mohamed Saïdi

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  1. Mohamed Saïdi
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Correspondence to Mohamed Saïdi.

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Saïdi, M. On the existence of non-geometric sections of arithmetic fundamental groups. Math. Z. 277, 361–372 (2014). https://doi.org/10.1007/s00209-013-1260-8

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  • DOI: https://doi.org/10.1007/s00209-013-1260-8

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