On an analogue of the Lutz-Nagell theorem for hyperelliptic curves

DOI10.1016/j.jnt.2012.02.023zbMath1310.11068OpenAlexW2091709843MaRDI QIDQ1932387

David Grant

Publication date: 18 January 2013

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.02.023

zbMATH Keywords

arithmetic of hyperelliptic curves

Mathematics Subject Classification ID

[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)] Global ground fields in algebraic geometry (14G25)

Related Items (4)

Generalized fruit Diophantine equation and hyperelliptic curves ⋮ Chabauty–Coleman Experiments for Genus 3 Hyperelliptic Curves ⋮ Infinitely many hyperelliptic curves with exactly two rational points ⋮ \(K_2\) of families of curves with non-torsion differences in divisorial support

Cites Work

• Integrality of torsion points on abelian varieties over \(p\)-adic fields
• \(S\)-units attached to genus 3 hyperelliptic curves
• A finiteness property of torsion points
• Courbes sur une variété abélienne et points de torsion
• Units from 5-torsion on the Jacobian of \(y^2=x^5+1/4\) and the conjectures of Stark and Rubin
• Points of finite order on elliptic curves over number fields
• An approximation property for Teichmüller points
• Abeliants and their application to an elementary construction of Jacobians.
• Class invariants for quartic CM fields
• Integral division points on curves
• The Arithmetic of Elliptic Curves
• Quelques propriétés arithmétiques des points de $3$-division de la jacobienne de $y^2 = x^5 - 1$
• Canonical heights on the Jacobians of curves of genus 2 and the infinite descent
• The Manin-Mumford Conjecture: A Brief Survey
• On a unit group generated by special values of Siegel modular functions
• Prime divisors of special values of theta functions in the ray class field of a certain quartic field modulo $2^n$
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