On reductions of Selmer sections
Algebraic Geometry
2025-09-22 v1
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.
Cite
@article{arxiv.2509.15660,
title = {On reductions of Selmer sections},
author = {Wojciech Porowski},
journal= {arXiv preprint arXiv:2509.15660},
year = {2025}
}