On the arithmetic of the curves \(y^2=x^l+A\). II

DOI10.1006/jnth.2001.2727zbMath1004.11038OpenAlexW2016699510MaRDI QIDQ1604983

Michael Stoll

Publication date: 10 July 2002

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

Full work available at URL: https://doi.org/10.1006/jnth.2001.2727

zbMATH Keywords

hyperelliptic curveJacobiancomplex multiplicationSelmer grouproot numberBirch and Swinnerton-Dyer Conjecture

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) [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)] (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (9)

ON SELMER GROUPS AND TATE–SHAFAREVICH GROUPS FOR ELLIPTIC CURVESy²=x³−n³ ⋮ Exhibiting SHA[2 on hyperelliptic Jacobians] ⋮ Ranks in the family of hyperelliptic Jacobians of \(y^2=x^5+ax\) ⋮ On the Jacobian of a family of hyperelliptic curves ⋮ Algebraic points on the hyperelliptic curves \(y^2 = x^5 + n^2\) ⋮ Note on the rank of quadratic twists of Mordell equations ⋮ Root numbers for the Jacobian varieties of Fermat curves ⋮ 3-Selmer groups for curves y 2 = x 3 + a ⋮ Ranks in the family of hyperelliptic Jacobians of y2 = x5 + ax II

Cites Work

• Some results on the Mordell-Weil group of the Jacobian of the Fermat curve
• The Cassels-Tate pairing on polarized Abelian varieties
• On the functional equation of the Artin L-function for characters of real representations
• On the arithmetic of the curves o y2 = xℓ + A and their Jacobians
• On the arithmetic of abelian varieties
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the arithmetic of the curves \(y^2=x^l+A\). II