no. 2
Holomorphic curves in compact Shimura varieties
Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 647-659.

We prove a hyperbolic analogue of the Bloch–Ochiai theorem about the Zariski closure of holomorphic curves in abelian varieties.

On démontre un analogue hyperbolique du théorème de Bloch–Ochiai sur l’adhérence de Zariski d’une courbe holomorphe dans une variété abélienne.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3174
Classification: 14G35,  32A10,  03C64
Keywords: Shimura variety, holomorphic curve, o-minimality 
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Ullmo, Emmanuel; Yafaev, Andrei. Holomorphic curves in compact Shimura varieties. Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 647-659. doi : 10.5802/aif.3174. https://aif.centre-mersenne.org/articles/10.5802/aif.3174/

[1] Alexander, Herbert Volumes of varieties in projective space and in Grassmannians, Trans. Am. Math. Soc., Tome 289 (1974), pp. 237-249 | Article | Zbl: 0285.32008

[2] Deligne, Pierre Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques, Automorphic forms, representations and L-functions (Corvallis, 1977) (Proceedings of Symposia in pure Mathematics) Tome 33 (1979), pp. 247-289 | Zbl: 0437.14012

[3] van den Dries, Lou Tame topology and o-minimal structures, London Mathematical Society Lecture Note Series, Tome 248, Cambridge University Press, 1998, x+180 pages | Zbl: 0953.03045

[4] Klingler, Bruno; Ullmo, Emmanuel; Yafaev, Andrei The hyperbolic Ax-Lindemann-Weierstrass conjecture, Publ. Math., Inst. Hautes Étud. Sci., Tome 123 (2016), pp. 333-360 | Article | Zbl: 1372.14016

[5] Kobayashi, Shoshichi Hyperbolic Complex Spaces, Grundlehren der Mathematischen Wissenschaften, Tome 318, Springer, 1998, xiii+471 pages | Zbl: 0917.32019

[6] Mok, Ngaiming Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds, Series in Pure Mathematics, Tome 6, World Scientific, 1989, xiv+278 pages | Zbl: 0912.32026

[7] Moonen, Ben Linearity properties of Shimura varieties. I., J. Algebr. Geom., Tome 7 (1998) no. 3, pp. 539-567 | Zbl: 0956.14016

[8] Pila, Jonathan; Wilkie, Alex J. The rational points of a definable set, Duke Math. J., Tome 133 (2006) no. 3, pp. 591-616 | Article | Zbl: 1217.11066

[9] Ullmo, Emmanuel Applications du theorème d’Ax-Lindemann hyperbolique, Compos. Math., Tome 150 (2014) no. 2, pp. 175-190 | Article | Zbl: 1326.14062

[10] Ullmo, Emmanuel; Andrei, Yafaev Hyperbolic Ax-Lindemann theorem in the co-compact case, Duke Math. J., Tome 163 (2014) no. 2, pp. 433-463 | Article | Zbl: 1375.14096

[11] Ullmo, Emmanuel; Andrei, Yafaev o-minimal flows on abelian varieties, Q. J. Math, Tome 163 (2017) no. 2, pp. 359-367 | Article | Zbl: 06798572

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