On a dynamical brauer-manin obstruction

Liang Chung Hsia, Joseph Silverman

研究成果: 雜誌貢獻期刊論文同行評審

6 引文 斯高帕斯(Scopus)

摘要

Let φ: X → X be a morphism of a variety defined over a number field K, let V ⊂ X be a K-subvariety, and let Oφ(P) = {φn(P): n ≥ 0} be the orbit of a point P ∈ X(K). We describe a local-global principle for the intersection V ∩ Oφ(P). This principle may be viewed as a dynamical analog of the Brauer- Manin obstruction. We show that the rational points of V (K) are Brauer-Manin unobstructed for power maps on ℙ2 in two cases: (1) V is a translate of a torus. (2) V is a line and P has a preperiodic coordinate. A key tool in the proofs is the classical Bang- Zsigmondy theorem on primitive divisors in sequences. We also prove analogous local-global results for dynamical systems associated to endomoprhisms of abelian varieties.

原文英語
頁(從 - 到)235-250
頁數16
期刊Journal de Theorie des Nombres de Bordeaux
21
發行號1
DOIs
出版狀態已發佈 - 2009
對外發佈

ASJC Scopus subject areas

  • 代數與數理論

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