Equidistribution of Frobenius eigenvalues

TL;DR

This paper investigates how Frobenius eigenvalues vary in families of algebraic curves over finite fields, providing insights into their distribution and behavior in algebraic geometry.

Contribution

It introduces new results on the equidistribution of Frobenius eigenvalues across families of algebraic curves over finite fields.

Findings

Frobenius eigenvalues exhibit equidistribution in certain families

Variation patterns of eigenvalues are characterized

Connections to algebraic geometry and number theory are established

Abstract

We study the problem of variation of Frobenius eigenvalues on the cohomology of families of local systems of algebraic curves over finite fields.