Degree gaps for multipliers and the dynamical André–Oort conjecture

DOI10.4153/S0008439520000892zbMath1487.37104arXiv2007.00567OpenAlexW3099765403WikidataQ122945741 ScholiaQ122945741MaRDI QIDQ5019193

Patrick Ingram

Publication date: 3 January 2022

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.00567

zbMATH Keywords

arithmetic dynamicsunlikely intersectionscritical height

Mathematics Subject Classification ID

Heights (11G50) Arithmetic properties of periodic points (37P35) Arithmetic dynamics on general algebraic varieties (37P55) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30) Families and moduli spaces in arithmetic and non-Archimedean dynamical systems (37P45)

Cites Work

• The dynamical André-Oort conjecture: unicritical polynomials
• The critical height is a moduli height
• Critical orbits of polynomials with a periodic point of specified multiplier
• A Case of the Dynamical André–Oort Conjecture
• SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS
• Variation of the canonical height for a family of polynomials
• Moduli Spaces and Arithmetic Dynamics
• A Finiteness Result for Post-critically Finite Polynomials
• Classification of Special Curves in the Space of Cubic Polynomials
• A Dynamical Variant of the André-Oort Conjecture
• Preperiodic points for families of rational maps
• Bifurcation measures and quadratic rational maps

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