\'Etale homotopy types of moduli stacks of polarised abelian schemes

TL;DR

This paper computes the étale homotopy types of moduli stacks of polarized abelian schemes, explores their arithmetic properties, and examines the Torelli morphism via étale homotopy methods.

Contribution

It provides the first determination of the étale homotopy types of these moduli stacks and analyzes the Torelli morphism from this perspective.

Findings

Determined étale homotopy types of moduli stacks

Derived arithmetic properties of étale fundamental groups

Analyzed Torelli morphism using étale homotopy methods

Abstract

We determine the Artin-Mazur \'etale homotopy types of moduli stacks of polarised abelian schemes using transcendental methods and derive some arithmetic properties of the \'etale fundamental groups of these moduli stacks. Finally we analyse the Torelli morphism between the moduli stacks of algebraic curves and principally polarised abelian schemes from an \'etale homotopy point of view.