Pseudo-Néron Model and Restriction of Sections

Abstract

We introduce the notion of pseudo-Néron model and give new examples of varieties admitting pseudo-Néron models other than Abelian varieties. As an application of pseudo-Néron models, given a scheme admitting a finite morphism to an Abelian scheme over a positive-dimensional base, we prove that for a very general genus-0 degree-d curve in the base with d sufficiently large, every section of the scheme over the curve is contained in a unique section over the entire base.