On the zero locus of normal functions and the \'etale Abel-Jacobi map

TL;DR

This paper explores the arithmetic properties of the zero locus of normal functions and their relation to the étale Abel-Jacobi map, providing criteria and comparison theorems.

Contribution

It introduces a criterion for the zero locus of a normal function to be defined over a number field and compares the Abel-Jacobi map with étale cohomology.

Findings

Criterion for zero locus definability over a number field

Comparison theorems between normal functions and étale Abel-Jacobi map

Insights into the arithmetic nature of Abel-Jacobi invariants

Abstract

We investigate questions of an arithmetic nature related to the Abel-Jacobi map. We give a criterion for the zero locus of a normal function to be defined over a number field, and we give some comparison theorems with the Abel-Jacobi map coming from continuous \'etale cohomology.