Abstract
We prove a hyperbolic analogue of the Bloch–Ochiai theorem about the Zariski closure of holomorphic curves in abelian varieties. We consider the case of non compact Shimura varieties completing the proof of the result for all Shimura varieties. The statement which we consider here was first formulated and proven by Ullmo and Yafaev for compact Shimura varieties.
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18 November 2019
This erratum addresses an error in the application of a theorem of Hwang and To in the cited paper.
18 November 2019
This erratum addresses an error in the application of a theorem of Hwang and To in the cited paper.
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Acknowledgements
I would like to thank my supervisor Andrei Yafaev for pointing me to this problem and some helpful discussions. I would also like to thank Jacob Tsimerman who was the first to point out that the result in Lemma 3.3 could be generalised from the cocompact case in [12] to the general case using the existence of a bounded realisation for \(\mathcal{D}\). Finally, I would like to thank Chirstopher Daw, Ziyang Gao, Jacob Tsimerman, and the referee for helpful comments on an earlier version of the paper.
This work was supported by the Engineering and Physical Sciences Research Council [EP/L015234/1]. The EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), University College London.
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Giacomini, M. Holomorphic curves in Shimura varieties. Arch. Math. 111, 379–388 (2018). https://doi.org/10.1007/s00013-018-1227-4
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DOI: https://doi.org/10.1007/s00013-018-1227-4