Bruno Klingler "Bi-algebraic geometry and some diophantine problems"

Bruno Klingler (Université Paris VII)
Bi-algebraic geometry and some diophantine problems

Bi-algebraic geometry is a simple geometric format encoding functional and arithmetical transcendence statements. In this talk, I will describe this format and its applications to two classical diophantine problems : the Manin-Mumford conjecture on the distribution of torsion points on Abelian varieties, and the André-Oort conjecture on the distribution of CM-points on Shimura varieties.