Seminar in Algebraic Geometry and Number Theory

Abstract: We study the variation of heights of cycles in flat families over number fields or, more generally, globally valued fields. To a finite type scheme over a GVF we associate a locally compact Hausdorff space which we refer to as its GVF analytification. We prove the continuity of heights in a flat family on the GVF analytification. As an application, we prove Roberto Gualdi's conjecture on limit heights of complete intersections in toric varieties. This is joint work with Pablo Destic and Michal Szachniewicz.