Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn)

DOI10.4171/JEMS/560zbMath1328.11068OpenAlexW2304248228MaRDI QIDQ747614

Umberto Zannier, David W. Masser

Publication date: 16 October 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/560

zbMATH Keywords

Pell equationJacobian varietytorsion pointabelian surface schemeChabauty's theorem

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Jacobians, Prym varieties (14H40) [https://zbmath.org/classification/?q=cc:11G30 Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Heights (11G50) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Arithmetic ground fields for abelian varieties (14K15)

Related Items

Betti maps, Pell equations in polynomials and almost-Belyi maps ⋮ Unnamed Item ⋮ Unlikely intersections for curves in products of Carlitz modules ⋮ Torsion hypersurfaces on abelian schemes and Betti coordinates ⋮ Pell surfaces ⋮ Generalized Jacobians and Pellian polynomials ⋮ Unlikely Intersections and Pell’s Equations in Polynomials ⋮ Unlikely intersections of curves with algebraic subgroups in semiabelian varieties ⋮ An overview on problems of unlikely intersections in families of abelian varieties ⋮ Unlikely intersections for curves in additive groups over positive characteristic ⋮ Tameness in geometry and arithmetic: beyond o-minimality ⋮ Greatest common divisor results on semiabelian varieties and a conjecture of Silverman ⋮ Quartic integral polynomial Pell equations ⋮ Diophantine approximations. Abstracts from the workshop held April 17--23, 2022 ⋮ Relative Manin–Mumford for Semi-Abelian Surfaces ⋮ Torsion points on families of products of elliptic curves ⋮ Relative Manin–Mumford in additive extensions ⋮ Density of algebraic points on Noetherian varieties ⋮ Generic rank of Betti map and unlikely intersections ⋮ A consequence of the relative Bogomolov conjecture ⋮ Basics on the theory of heights and its applications to certain Diophantine problems ⋮ Point counting for foliations over number fields ⋮ Unlikely intersections in semiabelian surfaces

Cites Work

• Effective Chabauty
• Cycles of quadratic polynomials and rational points on a genus-2 curve
• Unnamed Item
• Unnamed Item
• Unnamed Item