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arXiv · 2509.15660

On reductions of Selmer sections

Wojciech Porowski
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Abstract

We consider reductions of Selmer sections of the \'etale homotopy sequence of a hyperbolic curve over a number field. We show that the conjugacy class of a noncuspidal Selmer section is uniquely determined by its reduction on a set of density one. Moreover, we show that a noncuspidal Selmer section reduces to cusps only on a set of density zero, at least after a finite field extension.

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Wojciech Porowski. 2025-09-19. On reductions of Selmer sections. https://arxiv.org/abs/2509.15660

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