On the birational section conjecture with local conditions
成果类型：
Article
署名作者：
Stix, Jakob
署名单位：
Goethe University Frankfurt
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-014-0514-3
发表日期：
2015
页码：
239-265
关键词：
摘要：
A birationally liftable Galois section of a hyperbolic curve over a number field yields an adelic point of the smooth completion . We show that is -integral outside a set of places of Dirichlet density , or is cuspidal. The proof relies on -quotients of for some open . If is totally real or imaginary quadratic, we prove that all birationally adelic, non-cuspidal Galois sections come from rational points as predicted by the section conjecture of anabelian geometry. As an aside we also obtain a strong approximation result for rational points on hyperbolic curves over or imaginary quadratic fields.
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