Dr. Fabrizio Barroero (Roma Tre):
On the Zilber-Pink Conjecture for complex abelian varieties
Time and place
Friday, 14.2.20, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Abstract
The Zilber-Pink conjecture roughly says that the intersection of a subvariety of an abelian variety with its algebraic subgroups of large enough codimension is well behaved. In the case the subvariety has dimension 1, if the abelian variety and the subvariety are defined over the algebraic numbers, Habegger and Pila proved the conjecture, thus showing that the intersection of a curve with algebraic subgroups of codimension at least 2 is finite, unless the curve is contained in a proper algebraic subgroup. Together with Gabriel Dill, using a recent result of Gao, we extended this statement to complex abelian varieties. More generally, we showed that the whole conjecture for complex abelian varieties can be deduced from the algebraic case.\n