A Combination of the Conjectures of Mordell-Lang and André-Oort

By R. Pink. 2005

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Ax–Schanuel for the $j$-function (2014, unknown): “On the Zilber-Pink conjecture generally see [6, 24, 25, 29, 30].”
The Betti map associated to a section of an abelian scheme (2018, background): “The following heuristic dichotomy arises (see Pink’s conjectures, formulated in [29] and further discussed in [30]; see also the third author’s book [36], especially chapter 3): (A) When dimS < g, one expects under natural assumptions that ξAtors is contained in ⋃N n=1 ξ −1A[n] for some N , hence is”
Ax-Lindemann for $\mathcal{A}_g$ (2014, background): “We work exclusively with connected Shimura varieties, of which an excellent account can be found in [31].”
Towards the Andr\'e-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points (2013, background): “(Pink, [54, Definition 4.1(b)]) Let S be a connected mixed Shimura variety.”
O-minimality and certain atypical intersections (2014, background): “The Zilber-Pink Conjecture remains open for surfaces in abelian varieties defined over a number field.”
O-minimality and the André-Oort conjecture for $\mathbb{C}^{n}$ (2011, background): “A conjecture of Pink [73], [74] combines AO, MM and ML in a far-reaching generalization.”