We consider an irreducible curve in , where is an elliptic curve and and are both defined over . Assuming that is not contained in any translate of a proper algebraic subgroup of , we show that the points of the union , where ranges over all proper algebraic subgroups of , form a set of bounded canonical height. Furthermore, if has Complex Multiplication then the set , for ranging over all algebraic subgroups of of codimension at least , is finite. If has no Complex Multiplication then the set for ranging over all proper algebraic subgroups of of codimension at least , is finite.
@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}, pages = {47--75}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 2}, number = {1}, year = {2003}, mrnumber = {1990974}, zbl = {1170.11314}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2003_5_2_1_47_0/} }
TY - JOUR AU - Viada, Evelina TI - The intersection of a curve with algebraic subgroups in a product of elliptic curves JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 47 EP - 75 VL - 2 IS - 1 PB - Scuola normale superiore UR - http://archive.numdam.org/item/ASNSP_2003_5_2_1_47_0/ LA - en ID - ASNSP_2003_5_2_1_47_0 ER -
%0 Journal Article %A Viada, Evelina %T The intersection of a curve with algebraic subgroups in a product of elliptic curves %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 47-75 %V 2 %N 1 %I Scuola normale superiore %U http://archive.numdam.org/item/ASNSP_2003_5_2_1_47_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2003_5_2_1_47_0/
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