# Endomorphism Algebras of Abelian varieties with special reference to Superelliptic Jacobians

## TL;DR

This survey explores the endomorphism algebras of abelian varieties, especially superelliptic Jacobians, using Galois properties of torsion points to understand their structure and applications.

## Contribution

It provides a comprehensive overview of how Galois theory informs the endomorphism structures of abelian varieties, focusing on superelliptic Jacobians.

## Key findings

- Galois properties of torsion points reveal endomorphism algebra structures.
- Applications to cyclic covers of the projective line are detailed.
- The survey consolidates known results and methods in this area.

## Abstract

This is (mostly) a survey article. We use an information about Galois properties of points of small order on an abelian variety in order to describe its endomorphism algebra over an algebraic closure of the ground field. We discuss in detail applications to jacobians of cyclic covers of the projective line.