Rational points on hyperelliptic curves having a marked non-Weierstrass point

DOI10.1112/S0010437X17007515zbMath1387.11035arXiv1307.3531MaRDI QIDQ4590956

Xiaoheng Wang, Arul Shankar

Publication date: 21 November 2017

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.3531

zbMATH Keywords

rational pointshyperelliptic curvesSelmer groupsranks of abelian varieties

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)]

Related Items

An improvement on Schmidt’s bound on the number of number fields of bounded discriminant and small degree ⋮ Squarefree values of polynomial discriminants. I ⋮ Arithmetic statistics of Prym surfaces ⋮ A new parametrization for ideal classes in rings defined by binary forms, and applications ⋮ 2-Selmer groups of even hyperelliptic curves over function fields ⋮ On the squarefree values of \(a^4+b^3\) ⋮ Most odd-degree binary forms fail to primitively represent a square ⋮ Explicit methods in number theory. Abstracts from the workshop held July 18--24, 2021 (hybrid meeting) ⋮ \(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field ⋮ Average size of 2-Selmer groups of Jacobians of odd hyperelliptic curves over function fields ⋮ On the proportion of locally soluble superelliptic curves

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
• Most odd degree hyperelliptic curves have only one rational point
• \(p\)-adic and real subanalytic sets
• The density of discriminants of quintic rings and fields
• Effective Chabauty
• Squarefree values of polynomial discriminants. I
• The density of discriminants of quartic rings and fields
• Implementing 2-descent for Jacobians of hyperelliptic curves
• Average ranks of elliptic curves: Tension between data and conjecture
• Néron Models
• A.D. Alexandrov spaces with curvature bounded below
• Arithmetic invariant theory
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
• On a Principle of Lipschitz