Autour de la conjecture de Zilber-Pink
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 2, p. 405-414

We describe some results toward the following conjecture: if X is an irreducible subvariety of a semi-abelian variety A, its intersection with the union of all algebraic subgroups A of codimension greater than the dimension of X is not Zariski-dense in X, unless X is contained in a proper algebraic subgroup of A.

Nous dressons un rapide panorama de résultats allant dans le sens de la conjecture suivante : l’intersection d’une sous-variété X d’une variété semi-abélienne A et de l’union de tous les sous-groupes algébriques de A de codimension au moins dimX+1 n’est pas Zariski-dense dans X dès que X n’est pas contenue dans un sous-groupe algébrique strict de A.

@article{JTNB_2009__21_2_405_0,
     author = {R\'emond, Ga\"el},
     title = {Autour de la conjecture de Zilber-Pink},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {2},
     year = {2009},
     pages = {405-414},
     doi = {10.5802/jtnb.677},
     mrnumber = {2541432},
     zbl = {1196.11083},
     language = {fr},
     url = {http://www.numdam.org/item/JTNB_2009__21_2_405_0}
}
Rémond, Gaël. Autour de la conjecture de Zilber-Pink. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 2, pp. 405-414. doi : 10.5802/jtnb.677. http://www.numdam.org/item/JTNB_2009__21_2_405_0/

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