Pseudo-N\'eron Model and Restriction of Sections II, Generalization, Examples and Applications

TL;DR

This paper extends the class of families with restriction of sections theorems beyond Abelian varieties, providing new examples of pseudo-Néron models and exploring related counterexamples and applications to Hodge classes.

Contribution

It generalizes previous results on restriction of sections, introduces new examples of pseudo-Néron models, and discusses conditions related to rational curves and Hodge classes.

Findings

Broader class of families admit restriction of sections.

New examples of pseudo-Néron models provided.

Counterexamples show non-existence of rational curves is not necessary.

Abstract

This is the continuation of the article by the author that proves a broader class of families admitting the theorem of restriction of sections other than Abelian varieties and gives new examples of pseudo-N\'eron models. In this work, we show that the techniques in the first paper give more general results and more examples such that the theorem of restriction of sections holds. Also, we give counter examples to show that the non-existence of rational curves is not a necessary condition for such theorems. As an application, we prove a result for Hodge classes of a certain weight which is similar to the result about sections.