About the mixed André–Oort conjecture: Reduction to a lower bound for the pure case

Ziyang Gao

doi:10.1016/j.crma.2016.01.024

Number theory/Algebraic geometry

About the mixed André–Oort conjecture: Reduction to a lower bound for the pure case

Presented by: the Editorial Board

Ziyang Gao ¹

¹ Institut des hautes études scientifiques, Le Bois-Marie, 35, route de Chartres, 91440 Bures-sur-Yvette, France

Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 659-663.

Abstract
Résumé

We prove that the mixed André–Oort conjecture holds for any mixed Shimura variety if a lower bound for the size of Galois orbits of special points in pure Shimura varieties exists. This generalizes the current results for mixed Shimura varieties of Abelian type.

Nous démontrons la conjecture d'André–Oort pour toutes les variétés de Shimura mixtes, sous une borne inférieure pour la taille de orbites galoisiennes des points spéciaux. Ceci généralise les résultats connus pour les variétés de Shimura mixtes de type abélien.

Received: 2015-11-30
Accepted: 2016-01-28
Published online: 2016-05-16

DOI: 10.1016/j.crma.2016.01.024

Author's affiliations:

Ziyang Gao ¹

¹ Institut des hautes études scientifiques, Le Bois-Marie, 35, route de Chartres, 91440 Bures-sur-Yvette, France

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     title = {About the mixed {Andr\'e{\textendash}Oort} conjecture: {Reduction} to a lower bound for the pure case},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {659--663},
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     year = {2016},
     doi = {10.1016/j.crma.2016.01.024},
     language = {en},
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Ziyang Gao. About the mixed André–Oort conjecture: Reduction to a lower bound for the pure case. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 659-663. doi : 10.1016/j.crma.2016.01.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.024/

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