The arithmetic of curves defined by iteration

DOI10.4064/aa169-1-1zbMath1330.14032arXiv1305.0222OpenAlexW2963495552MaRDI QIDQ5252463

Wade Hindes

Publication date: 1 June 2015

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0222

zbMATH Keywords

rational points on curvesquadratic polynomialdynamical arboreal representationHall-Lang conjecture

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Rational points (14G05) Elliptic curves over global fields (11G05) Arithmetic ground fields for curves (14H25) Special algebraic curves and curves of low genus (14H45) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Groups acting on trees (20E08) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Arithmetic dynamics on general algebraic varieties (37P55) Dynamical systems over global ground fields (37P15)

Related Items (4)

Rational points on certain families of symmetric equations ⋮ Finite index theorems for iterated Galois groups of cubic polynomials ⋮ Classifying Galois groups of small iterates via rational points ⋮ The Vojta conjecture implies Galois rigidity in dynamical families

Uses Software

• Magma
• SageMath

Cites Work

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• The Mordell–Weil sieve: proving non-existence of rational points on curves
• Jacobians with complex multiplication
• The density of prime divisors in the arithmetic dynamics of quadratic polynomials
• Points on elliptic curves parametrizing dynamical Galois groups
• Decomposing Jacobians of curves with extra automorphisms

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