The numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension

TL;DR

This paper proves the numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension, advancing understanding in algebraic geometry and related mathematical fields.

Contribution

It establishes the conjecture for a specific class of abelian varieties, extending previous results and providing new insights into their geometric properties.

Findings

Proved the conjecture for squares of simple abelian varieties of prime dimension

Extended results to some related cases

Contributed to the understanding of algebraic cycles and Hodge theory

Abstract

We prove the numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension, and also in some related cases.