no. 2
Holomorphic curves in compact Shimura varieties
Ullmo, Emmanuel1; Yafaev, Andrei2
1 IHES and Universite Paris-Saclay 35 Route de Chartres, 91440 Bures-sur-Yvette (France)
2 UCL, Department of Mathematics, Gower street, WC1E 6BT, London (UK)
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
Mot clés : variété de Shimura, courbes holomorphiques, o-minimalité
Ullmo, Emmanuel 1; Yafaev, Andrei 2

1 IHES and Universite Paris-Saclay 35 Route de Chartres, 91440 Bures-sur-Yvette (France)
2 UCL, Department of Mathematics, Gower street, WC1E 6BT, London (UK)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{AIF_2018__68_2_647_0,
     author = {Ullmo, Emmanuel and Yafaev, Andrei},
     title = {Holomorphic curves in compact {Shimura} varieties},
     journal = {Annales de l'Institut Fourier},
     pages = {647--659},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {68},
     number = {2},
     year = {2018},
     doi = {10.5802/aif.3174},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3174/}
}
TY  - JOUR
AU  - Ullmo, Emmanuel
AU  - Yafaev, Andrei
TI  - Holomorphic curves in compact Shimura varieties
JO  - Annales de l'Institut Fourier
PY  - 2018
SP  - 647
EP  - 659
VL  - 68
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.3174/
DO  - 10.5802/aif.3174
LA  - en
ID  - AIF_2018__68_2_647_0
ER  - 
%0 Journal Article
%A Ullmo, Emmanuel
%A Yafaev, Andrei
%T Holomorphic curves in compact Shimura varieties
%J Annales de l'Institut Fourier
%D 2018
%P 647-659
%V 68
%N 2
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.3174/
%R 10.5802/aif.3174
%G en
%F AIF_2018__68_2_647_0
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., Volume 289 (1974), pp. 237-249 | DOI | Zbl

[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), Volume 33 (1979), pp. 247-289 | Zbl

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

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

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

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

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

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

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

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

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

Cited by Sources: