2019/01/01 by Yongqi Liang, Liang, Yongqi
Engineering · Mathematics · Social Sciences · #11G35 #14G25 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Vietnamese History and Culture Studies
paper · pdf · doi:10.48550/arxiv.1901.00118
openalex publication_date 2019/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider strong approximation for algebraic varieties defined over a number field k. Let S be a finite set of places of k containing all archimedean places. Let E be an elliptic curve of positive Mordell-Weil rank and let A be an abelian variety of positive dimension and of finite Mordell-Weil group. For an arbitrary finite set \mathfrakT of torsion points of E× A, denote by X its complement. Supposing the finiteness of Sha(E× A), we prove that X satisfies strong approximation with Brauer-Manin obstruction off S if and only if the projection of \mathfrakT to A contains no k-rational points.