Holomorphic curves in Shimura varieties

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Date(s) - 15/01/2019
11 h 00 min - 12 h 00 min


The Bloch-Ochiai theorem states that the Zariski closure of an holomorphic curve in an abelian variety is a translate of an abelian subvariey. In this talk we will present an anaogue of this result for Shimura varieties, the formulation of which was first proposed, and proved in the cocompact case, by Ullmo and Yafaev; along with the Bloch-Ociai theorem, it draws inspiration from the hyperbolic Ax-Lindemann-Weierstrass theorem. We will present the main points of the proof, which relies on the Ax-Lindemann-Weierstass theorem as well as the Pila-Wilkie counting theorem for sets definable in o-minimal structures. No prior knowledge of the topics will be assumed.


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