Unlikely intersections in products of families of elliptic curves and\n the multiplicative group

2016/06/07 by Fabrizio Barroero, Barroero, Fabrizio, Laura Capuano +1 · 1 citation
Mathematics · #11G05 #11U09 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1606.02063

openalex publication_date 2016/06/07 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let E_\λ be the Legendre elliptic curve of equation\nY²=X(X-1)(X-\λ). We recently proved that, given n linearly\nindependent points P₁(\λ), \…,P_n(\λ) on E_\λ with\ncoordinates in \\ℚ(\λ), there are at most finitely many\ncomplex numbers \λ₀ such that the points P₁(\λ₀),\n\…,P_n(\λ₀) satisfy two independent relations on E_\λ0. In\nthis article we continue our investigations on Unlikely Intersections in\nfamilies of abelian varieties and consider the case of a curve in a product of\ntwo non-isogenous families of elliptic curves and in a family of split\nsemi-abelian varieties.\n

Citations

• Geometric categories and o-minimal structures
• Torsion points on families of squares of elliptic curves
• Courbes sur une vari�t� ab�lienne et points de torsion
• Torsion points on families of products of elliptic curves

Cited by

• Singular intersections in families of abelian varieties

Related

• Unlikely and just likely intersections for high dimensional families of elliptic curves
• Isogeny relations in products of families of elliptic curves
• Unlikely intersections in families of abelian varieties and the polynomial Pell equation
• Singular intersections in families of abelian varieties
• Nice elliptic curves