# Rational points and derived equivalence

## TL;DR

This paper presents the first known examples of derived equivalences between varieties over non-closed fields, where one has a rational point and the other does not, highlighting new phenomena in arithmetic geometry.

## Contribution

It constructs explicit examples of derived equivalent varieties over non-closed fields with differing rational point properties, including torsors over Jacobians and hyperkähler 4-folds.

## Key findings

- Derived equivalences can occur between varieties with different rational point properties.
- Examples include torsors over Jacobians over Q and F_q(t).
- Hyperkähler 4-folds over Q exhibit a transcendental Brauer-Manin obstruction.

## Abstract

We give the first examples of derived equivalences between varieties defined over non-closed fields where one has a rational point and the other does not. We begin with torsors over Jacobians of curves over Q and F_q(t), and conclude with a pair of hyperkaehler 4-folds over Q. The latter is independently interesting as a new example of a transcendental Brauer-Manin obstruction to the Hasse principle.