Various results have been established towards the full conjecture by Ben Moonen, Yves André, Andrei Yafaev, Bas Edixhoven, Laurent Clozel, Bruno Klingler and Emmanuel Ullmo, among others.
In fact, the proof of the full conjecture under GRH was published by Bruno Klingler, Emmanuel Ullmo and Andrei Yafaev in 2014 in the Annals of Mathematics.
[3] In 2006, Umberto Zannier and Jonathan Pila used techniques from o-minimal geometry and transcendental number theory to develop an approach to the Manin-Mumford-André-Oort type of problems.
In 2009, Jonathan Pila proved the André-Oort conjecture unconditionally for arbitrary products of modular curves,[4][5] a result which earned him the 2011 Clay Research Award.
[citation needed] For the case of the Siegel modular variety, this bound was deduced by Jacob Tsimerman in 2015 from the averaged Colmez conjecture and the Masser-Wustholtz isogeny estimates.