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he Andre-Oort conjecture for Ag, under GRH, after Pila and Tsimerman

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Bas Edixhoven (Universiteit Leiden)

What
  • SFB-Kolloquium
When Jun 18, 2014
from 10:15 am to 11:15 am
Where Mainz, 05-432 (Hilbertraum)
Contact Name Ariyan Javanpeykar
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In their arxiv preprint of June 2012 Jonathan Pila and Jacob Tsimerman prove that the Andre-Oort conjecture for the moduli spaces of principally polarised abelian varieties is a consequence of the generalised Riemann hypothesis for number fields. I will discuss their proof. Some essential ingredients are the so-called Ax-Lindemann theorem, proved in the same article, the "counting theorems'' by Pila and Wilkie, and a lower bound for the number of points in Galois orbits of CM-points by Tsimerman. Unfortunately I have not yet studied more recent work by Klingler, Ulmmo and Yafaev on the Ax-Lindemann conjecture for general Shimura varieties, and the generalisation to mixed Shimura varieties by Ziyang Gao.