The André–Oort conjecture for Drinfeld modular varieties

Florian Breuer

doi:10.1016/j.crma.2007.05.008

Number Theory

The André–Oort conjecture for Drinfeld modular varieties

Presented by: Laurent Lafforgue

Florian Breuer ¹

¹ Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa

Comptes Rendus. Mathématique, Volume 344 (2007) no. 12, pp. 733-736.

Abstract
Résumé

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.

Received: 2007-02-15
Accepted: 2007-05-04
Published online: 2007-06-15

DOI: 10.1016/j.crma.2007.05.008

Author's affiliations:

Florian Breuer ¹

¹ Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa

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     title = {The {Andr\'e{\textendash}Oort} conjecture for {Drinfeld} modular varieties},
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     doi = {10.1016/j.crma.2007.05.008},
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Florian Breuer. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.05.008/

References
Cited by

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

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

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

[4] B. Moonen 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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