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

Abstract

Let Eλbe the Legendre elliptic curve of equation Y2= X (X - 1)(X - l). We recently proved that, given n linearly independent points P1(l), ¼, Pn(l) on Eλwith coordinates in (l), there are at most finitely many complex numbers l0such that the points P1(l0), ¼, Pn(l0) satisfy two independent relations on El0. In this article, we continue our investigations on Unlikely Intersections in families of abelian varieties, and consider the case of a curve in a product of two non-isogenous families of elliptic curves and in a family of split semi-abelian varieties

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Archivio della Ricerca - Università di Roma 3

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Last time updated on 06/01/2019

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