2020/10/10 by Han Wu, Wu, Han · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2010.04919
openalex publication_date 2020/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we construct three kinds of Châtelet surfaces, which have some given arithmetic properties with respect to field extensions of number fields. We then use these constructions to study the properties of weak approximation with Brauer-Manin obstruction and the Hasse principle with Brauer-Manin obstruction for 3-folds, which are pencils of Châtelet surfaces parameterized by a curve, with respect to field extensions of number fields. We give general constructions (conditional on a conjecture of M. Stoll) to negatively answer some questions, and illustrate these constructions and some exceptions with some explicit unconditional examples.