Applications du théorème d’Ax–Lindemann hyperbolique

By E. Ullmo. Compositio Mathematica, 2013

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The hyperbolic Ax-Lindemann-Weierstraß conjecture (2015, unknown): “Notice also that (as explained in [30]) a new proof of the André-Oort conjecture under the GRH, alternative to [31] and [12], is a consequence of three ingredients: Theorem 1.”
Hyperbolic Ax–Lindemann theorem in the cocompact case (2012, background): “Some applications of the hyperbolic Ax-Lindemann conjecture to the set of positive dimentional special subvarieties of subvarieties of Shimura varieties and an inconditional proof of the André-Oort conjecture for subvarieties of projective Shimura varieties in A6 are given in the recent preprint by ”
Applications of the hyperbolic Ax–Schanuel conjecture (2017, unknown): “ counting theorem. To do so, we formulate several arithmetic conjectures that are inspired by previous applications of the Pila-Zannier strategy. In this vein, our paper is very much in the spirit of [38], which, at the time, reduced the André-Oort conjecture to a point counting problem and then exp”
On the distribution of the Hodge locus (2021, methodology): “The proof is mainly inspired by the arguments appearing in [60, Theorem 4.1], [8, Theorem 1.2.1] and the work of Daw and Ren [19].”