Work

On the section conjecture over fields of finite type

Year: 2025

Type: article

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 . This class contains every projective, hyperelliptic curve, every hyperbolic, affine curve of genus , and a basis of open subsets 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 .

Source: Mathematische Nachrichten

DOI: 10.1002/mana.70049

Author: Giulio Bresciani

Institution: Scuola Normale Superiore

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,460

Funder: Deutsche Forschungsgemeinschaft