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.
We state an analogue of the André–Oort conjecture for subvarieties of Drinfeld modular varieties, and prove it in two special cases.
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@article{CRMATH_2007__344_12_733_0, author = {Breuer, Florian}, title = {The {Andr\'e{\textendash}Oort} conjecture for {Drinfeld} modular varieties}, journal = {Comptes Rendus. Math\'ematique}, pages = {733--736}, publisher = {Elsevier}, volume = {344}, number = {12}, year = {2007}, doi = {10.1016/j.crma.2007.05.008}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.05.008/} }
TY - JOUR AU - Breuer, Florian TI - The André–Oort conjecture for Drinfeld modular varieties JO - Comptes Rendus. Mathématique PY - 2007 SP - 733 EP - 736 VL - 344 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.05.008/ DO - 10.1016/j.crma.2007.05.008 LA - en ID - CRMATH_2007__344_12_733_0 ER -
%0 Journal Article %A Breuer, Florian %T The André–Oort conjecture for Drinfeld modular varieties %J Comptes Rendus. Mathématique %D 2007 %P 733-736 %V 344 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.05.008/ %R 10.1016/j.crma.2007.05.008 %G en %F CRMATH_2007__344_12_733_0
Breuer, Florian. The André–Oort conjecture for Drinfeld modular varieties. Comptes Rendus. Mathématique, Tome 344 (2007) no. 12, pp. 733-736. doi : 10.1016/j.crma.2007.05.008. http://archive.numdam.org/articles/10.1016/j.crma.2007.05.008/
[1] 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] Drinfeld modular polynomials in higher rank (Preprint available at) | arXiv
[3] Subvarieties of Shimura varieties, Ann. of Math., Volume 157 (2003) no. 2, pp. 621-645
[4] 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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