Geometric Bogomolov conjecture for nowhere degenerate abelian varieties of dimension $5$ with trivial trace

TL;DR

This paper proves the geometric Bogomolov conjecture for certain 5-dimensional nowhere degenerate abelian varieties with trivial trace, advancing understanding of the conjecture in specific geometric contexts.

Contribution

It establishes the conjecture for 5-dimensional cases with trivial trace, extending previous results to a new class of abelian varieties.

Findings

Proves the conjecture for 5-dimensional nowhere degenerate abelian varieties with trivial trace.

Shows the conjecture holds when the difference in dimensions of certain subvarieties equals 5.

Extends the class of abelian varieties for which the conjecture is verified.

Abstract

We prove that the geometric Bogomolov conjecture holds for nowhere degenerate abelian varieties of dimension $5$ with trivial trace. By this result together with our previous work, we see that the conjecture holds for an abelian variety such that the difference between the dimension of its maximal nowhere degenerate abelian subvariety and that of its trace equals $5$.