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arXiv · 1909.08318

The cuspidalisation of sections of arithmetic fundamental groups II

Mohamed Saidi
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Abstract

In this paper we investigate the theory of cuspidalisation of sections of arithmetic fundamental groups of hyperbolic curves to cuspidally i-th and 2/p-th step prosolvable arithmetic fundamental groups. As a consequence we exhibit two, necessary and sufficient, conditions for sections of arithmetic fundamental groups of hyperbolic curves over p-adic local fields to arise from rational points. We also exhibit a class of sections of arithmetic fundamental groups of p-adic curves which are orthogonal to Pic, and which satisfy (unconditionally) one of the above conditions.

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Mohamed Saidi. 2019-09-18. The cuspidalisation of sections of arithmetic fundamental groups II. https://doi.org/10.1016/j.aim.2019.106737

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