Seminari del Dipartimento
Geometria Unlikely intersections with isogeny orbits Dr. Gabriel Dill 14-03-2019 - 14:30 Largo San Leonardo Murialdo,1 - Pal.C - Aula 211
In the spirit of the Mordell-Lang conjecture, we consider the intersection of a closed irreducible algebraic subvariety V of a non-isotrivial abelian scheme over a smooth irreducible base curve with the images of a finite-rank subgroup Gamma of a fixed abelian variety A_0 under all isogenies between A_0 and some member of the family, where everything is defined over the field of algebraic numbers. After excluding certain degenerate cases, the André-Pink-Zannier conjecture predicts that this intersection is not Zariski dense in V. We present our results towards and sometimes beyond this conjecture under restrictions on either the dimension of V or the abelian scheme and A_0. |