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arXiv · 1911.03234

On the section conjecture over fields of finite type

Giulio Bresciani
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Abstract

Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of $\mathbb{Q}$. This class contains every projective, hyperelliptic curve, every hyperbolic, affine curve of genus $\le 2$, and a non-empty open subset of any curve. If we furthermore assume the weak Bombieri-Lang conjecture, we prove that the section conjecture holds for every hyperbolic curve over every finitely generated extension of $\mathbb{Q}$.

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Giulio Bresciani. 2023-03-01. On the section conjecture over fields of finite type. https://arxiv.org/abs/1911.03234

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