Yuri Bilu (U Bordeaux)
Tuesday, February 13, 2018 - 13:15
Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin-Adlershof, 006, Haus 3, Erdgeschoss
Forschungsseminar Arithmetische Geometrie
Prof. Jürg Kramer / Prof. Thomas Krämer
A singular modulus is the j-invariant of an elliptic curve with complex multiplication. André (1998) proved that a polynomial equation F(x,y)=0 can have only finitely many solutions in singular moduli (x,y), unless the polynomial F(x,y) is "special" in a certain precisely defined sense. Pila (2011) extended this to equations in many variables, proving the André-Oort conjecture on C^n. The arguments of André and Pila were non-effective (used Siegel-Brauer). I will report on a recent work by Allombert, Faye, Kühne, Luca, Masser, Pizarro, Riffaut, Zannier and myself about partial effectivization of these results.
submitted by Marion Thomma (thomma@math.hu-berlin.de, 2093-5815)