Relative Manin–Mumford in additive extensions

DOI10.1090/tran/7612zbMath1470.11189OpenAlexW2808311648MaRDI QIDQ4633629

Harry Schmidt

Publication date: 3 May 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/tran/7612

zbMATH Keywords

abelian varietiesPell's equationManin-Mumfordelliptic families

Mathematics Subject Classification ID

Elliptic curves (14H52) Heights (11G50) Classical hypergeometric functions, ({}_2F_1) (33C05) Group schemes (14L15) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (6)

Rational values of transcendental functions and arithmetic dynamics ⋮ Betti maps, Pell equations in polynomials and almost-Belyi maps ⋮ Pfaffian definitions of Weierstrass elliptic functions ⋮ Point counting for foliations over number fields ⋮ On the torsion values for sections of an elliptic scheme ⋮ Counting rational points and lower bounds for Galois orbits

Cites Work

• Sharpening `Manin-Mumford' for certain algebraic groups of dimension 2
• Rational values of the Riemann zeta function
• Torsion points on families of squares of elliptic curves
• Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn)
• Generalized Jacobians and Pellian polynomials
• Autour d'une conjecture de Serge Lang. (Around a conjecture by Serge Lang)
• \(p\)-adic interpolation of real analytic Eisenstein series
• Points of small height on elliptic curves
• Bicyclotomic polynomials and impossible intersections
• Torsion points on families of products of elliptic curves
• The number of integral points on arcs and ovals
• Torsion points, Pell's equation, and integration in elementary terms
• Special points on fibered powers of elliptic surfaces
• Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)
• Unlikely Intersections and Pell’s Equations in Polynomials
• Relative Manin–Mumford for Semi-Abelian Surfaces
• EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE
• A Combination of the Conjectures of Mordell-Lang and André-Oort
• On unlikely intersections of complex varieties with tori
• Elliptic Curves
• Heights and the specialization map for families of abelian varieties.
• Integer points on the dilation of a subanalytic surface
• The solution of the problem of integration in finite terms
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