Number Theory
The André–Oort conjecture for Drinfeld modular varieties
Comptes Rendus. Mathématique, Volume 344 (2007) no. 12, pp. 733-736.

We state an analogue of the André–Oort conjecture for subvarieties of Drinfeld modular varieties, and prove it in two special cases.

Nous énoncons un analogue de la conjecture d'André–Oort pour les sous-variétées des variétées modulaires de Drinfeld, et nous le démontrons dans deux cas.

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Published online:
DOI: 10.1016/j.crma.2007.05.008
Breuer, Florian 1

1 Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa
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Breuer, Florian. The André–Oort conjecture for Drinfeld modular varieties. Comptes Rendus. Mathématique, Volume 344 (2007) no. 12, pp. 733-736. doi : 10.1016/j.crma.2007.05.008. http://www.numdam.org/articles/10.1016/j.crma.2007.05.008/

[1] Breuer, F.; Pink, R. Monodromy groups associated to non-isotrivial Drinfeld modules in generic characteristic (van der Geer, G.; Moonen, B.; Schoof, R., eds.), Number Fields and Function Fields: Two Parallel Worlds, Progress in Mathematics, vol. 239, Birkhäuser, Basel, 2005

[2] Breuer, F.; Rück, H.-G. Drinfeld modular polynomials in higher rank (Preprint available at) | arXiv

[3] Edixhoven, S.J.; Yafaev, A. Subvarieties of Shimura varieties, Ann. of Math., Volume 157 (2003) no. 2, pp. 621-645

[4] Moonen, B. Linearity properties of Shimura varieties II, Compos. Math., Volume 114 (1998), pp. 3-35

[5] R. Noot, Correspondances de Hecke, action de Galois et la conjecture de André–Oort [d'après Edixhoven et Yafaev], Seminaire Bourbaki, Exposée n° 942, Novembre 2004

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