Unlikely Intersections and Pell’s Equations in Polynomials

DOI10.1007/978-3-319-05254-0_12zbMath1367.11037OpenAlexW317803994MaRDI QIDQ2948981

Umberto Zannier

Publication date: 7 October 2015

Published in: Trends in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-05254-0_12

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Global ground fields in algebraic geometry (14G25) Algebraic theory of abelian varieties (14K05) Arithmetic aspects of dessins d'enfants, Bely? theory (11G32)

Related Items (8)

Betti maps, Pell equations in polynomials and almost-Belyi maps ⋮ Torsion hypersurfaces on abelian schemes and Betti coordinates ⋮ Pell surfaces ⋮ Generalized Jacobians and Pellian polynomials ⋮ Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell–Lang conjecture ⋮ Relative Manin–Mumford in additive extensions ⋮ Generic rank of Betti map and unlikely intersections ⋮ Basics on the theory of heights and its applications to certain Diophantine problems

Cites Work

• Torsion points on families of squares of elliptic curves
• Twists and generalized Zolotarev polynomials.
• Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn)
• Torsion anomalous points and families of elliptic curves
• Small points and Arakelov theory
• Endomorphism estimates for abelian varieties
• Betti numbers of congruence groups. (Appendix: On representations of compact \(p\)-adic groups by Ze'ev Rudnick)
• Quasi-elliptic integrals and periodic continued fractions
• Genus one curves defined by separated variable polynomials and a polynomial Pell equation
• Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)
• Relative Manin–Mumford for Semi-Abelian Surfaces
• EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE
• On some problems of the arithmetical theory of continued fractions
• A Combination of the Conjectures of Mordell-Lang and André-Oort
• Fields of definition of function fields and hurwitz families — groups as galois groups
• Some remarks on the S-unit equation in function fields
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