# Derived equivalences of Abelian varieties and symplectic isomorphisms

## TL;DR

This paper investigates the relationship between derived equivalences of Abelian varieties and symplectic isomorphisms, proving a key surjectivity result for simple Abelian varieties over algebraically closed fields of characteristic zero.

## Contribution

It establishes that the natural correspondence between derived equivalences and symplectic isomorphisms is surjective for simple Abelian varieties, advancing understanding of their symplectic data.

## Key findings

- Proves surjectivity of the correspondence for simple Abelian varieties.
- Links derived equivalences to symplectic isomorphisms.
- Enhances classification of Abelian varieties via symplectic data.

## Abstract

We study derived equivalences of Abelian varieties in terms of their associated symplectic data. For simple Abelian varieties over an algebraically closed field of characteristic zero we prove that the natural correspondence introduced by Orlov, which maps equivalences to symplectic isomorphisms, is surjective.