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, p. 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
@article{ASNSP_2003_5_2_1_47_0,
     author = {Viada, Evelina},
     title = {The intersection of a curve with algebraic subgroups in a product of elliptic curves},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 2},
     number = {1},
     year = {2003},
     pages = {47-75},
     zbl = {1170.11314},
     mrnumber = {1990974},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2003_5_2_1_47_0}
}
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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