Normal Functions over Locally Symmetric Varieties

TL;DR

This paper classifies certain Hermitian variations of Hodge structure that admit infinitesimal normal functions and explores implications for cycle-class maps in families of abelian varieties with specific Mumford-Tate groups.

Contribution

It provides a classification of Hermitian real variations of Hodge structure with infinitesimal normal functions and analyzes their impact on cycle-class maps in abelian variety families.

Findings

Classification of Hermitian real variations of Hodge structure with infinitesimal normal functions

Implications for cycle-class maps on families of abelian varieties

Results related to Mumford-Tate groups

Abstract

We classify the irreducible Hermitian real variations of Hodge structure admitting an infinitesimal normal function, and draw conclusions for cycle-class maps on families of abelian varieties with a given Mumford-Tate group.