On the birational section conjecture with strong birationality assumptions
成果类型：
Article; Early Access
署名作者：
Bresciani, Giulio
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-023-01220-6
发表日期：
2023
关键词：
摘要：
Let X be a curve over a field k finitely generated over Q and t an indeterminate. We prove that, if s is a section of pi(1)(X) -> Gal(k) such that the base change s(k(t)) is birationally liftable, then s comes from geometry. As a consequence we prove that the section conjecture is equivalent to the cuspidalization of all sections over all finitely generated fields.