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A weak Néron model with applications to $p$ -adic dynamical systems

Liang-Chung Hsia — 1996

Compositio Mathematica

Weak Néron models for cubic polynomial maps over a non-Archimedean field

Jean-Yves Briend; Liang-Chung Hsia — 2012

Acta Arithmetica

Torsion points in families of Drinfeld modules

Dragos Ghioca; Liang-Chung Hsia — 2013

Acta Arithmetica

Let $Φ^{λ}$ be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for $Φ^{λ}$ for all λ. If there exist infinitely many λ ∈ K̅ such that both a(λ) and b(λ) are torsion points for $Φ^{λ}$ , then we show that for each λ ∈ K̅, a(λ) is torsion for $Φ^{λ}$ if and only if b(λ) is torsion for $Φ^{λ}$ . In the case a,b ∈ K, we prove in addition that a and b must be $̅_{p}$ -linearly dependent.

On a dynamical Brauer–Manin obstruction

Liang-Chung Hsia; Joseph Silverman — 2009

Journal de Théorie des Nombres de Bordeaux

Let $ϕ : X \to X$ be a morphism of a variety defined over a number field $K$ , let $V \subset X$ be a $K$ -subvariety, and let $𝒪_{ϕ} (P) = {ϕ^{n} (P) : n \geq 0}$ be the orbit of a point $P \in X (K)$ . We describe a local-global principle for the intersection $V \cap 𝒪_{ϕ} (P)$ . 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 $ℙ^{2}$ 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...

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Currently displaying 1 – 4 of 4

A weak Néron model with applications to $p$ -adic dynamical systems

Weak Néron models for cubic polynomial maps over a non-Archimedean field

Torsion points in families of Drinfeld modules

On a dynamical Brauer–Manin obstruction

Advanced Search

Formula preview

Currently displaying 1 – 4 of 4

A weak Néron model with applications to p -adic dynamical systems

Weak Néron models for cubic polynomial maps over a non-Archimedean field

Torsion points in families of Drinfeld modules

On a dynamical Brauer–Manin obstruction

A weak Néron model with applications to $p$ -adic dynamical systems