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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Approximation forte sur un produit de variétés abéliennes épointé en des points de torsion
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by Yongqi Liang PDF
Proc. Amer. Math. Soc. 148 (2020), 4635-4642 Request permission


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 $\mathfrak {T}$ of torsion points of $E\times A$, denote by $X$ its complement. Supposing the finiteness of ${\amalg \kern -.25pc\amalg } (E\times A)$, we prove that $X$ satisfies strong approximation with Brauer–Manin obstruction off $S$ if and only if the projection of $\mathfrak {T}$ to $A$ contains no $k$-rational points.
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Additional Information
  • Yongqi Liang
  • Affiliation: School of Mathematical Sciences, University of Science and Technology of China, 96 Jinzhai Road, 230026 Hefei, Anhui, People’s Republic of China
  • MR Author ID: 985656
  • Email:
  • Received by editor(s): May 12, 2019
  • Received by editor(s) in revised form: December 16, 2019, and January 18, 2020
  • Published electronically: July 30, 2020
  • Additional Notes: Ce travail est partiellement financié par Anhui Initiative in Quantum Information Technologies No. AHY150200.
  • Communicated by: Romyar T. Sharifi
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 4635-4642
  • MSC (2010): Primary 11G35, 14G25
  • DOI:
  • MathSciNet review: 4143382