Unlikely Intersections Seminar
Gabriel Dill
Leibniz Universität Hannover
Distinguished Categories: an Axiomatic Framework for Unlikely Intersections
Abstract: I will present joint work with Fabrizio Barroero (Roma Tre), in which we develop the axiomatic framework of distinguished and very distinguished categories for studying unlikely intersections (over a fixed algebraically closed ground field of characteristic 0). In distinguished categories, one can define special and weakly special subvarieties and formulate a Zilber-Pink statement. (Semi-)Abelian varieties and algebraic tori as well as pure and mixed Shimura varieties all form distinguished categories and the aforementioned notions specialize to the usual ones in these cases. We prove that the Zilber-Pink statement for a very distinguished category implies the same statement over any algebraically closed field extension of the ground field. This yields new instances of the Zilber-Pink conjecture in semiabelian varieties as well as in (mixed) Shimura varieties. Time permitting, I will finish by mentioning work in progress on generalized Hecke orbits in distinguished categories.
Tuesday November 8, 2022 at 2:00 PM in Zoom