The intersection of a curve with algebraic subgroups in a product of elliptic curves
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 1, pp. 47-75.

We consider an irreducible curve 𝒞 in E n , where E is an elliptic curve and 𝒞 and E are both defined over ¯. Assuming that 𝒞 is not contained in any translate of a proper algebraic subgroup of E n , we show that the points of the union 𝒞A( ¯), where A ranges over all proper algebraic subgroups of E n , form a set of bounded canonical height. Furthermore, if E has Complex Multiplication then the set 𝒞A( ¯), for A ranging over all algebraic subgroups of E n of codimension at least 2, is finite. If E has no Complex Multiplication then the set 𝒞A( ¯) for A ranging over all proper algebraic subgroups of E n of codimension at least n 2+2, is finite.

Classification: 11D45, 11G50
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Viada, Evelina. The intersection of a curve with algebraic subgroups in a product of elliptic curves. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 1, pp. 47-75. http://www.numdam.org/item/ASNSP_2003_5_2_1_47_0/

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