On a dynamical brauer-manin obstruction

Liang Chung Hsia, Joseph Silverman

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)235-250
Number of pages16
JournalJournal de Theorie des Nombres de Bordeaux
Volume21
Issue number1
DOIs
Publication statusPublished - 2009 Jan 1

ASJC Scopus subject areas

  • Algebra and Number Theory

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