The Brauer group is not a derived invariant

TL;DR

This paper shows that the Brauer group can differ for derived-equivalent Calabi-Yau 3-folds, indicating it is not a derived invariant, using topological K-theory techniques.

Contribution

It demonstrates that the Brauer group is not preserved under derived equivalence for Calabi-Yau 3-folds, providing new insights into their invariants.

Findings

Derived-equivalent Calabi-Yau 3-folds can have different Brauer groups

The difference is established using topological K-theory methods

This shows the Brauer group is not a derived invariant.

Abstract

In this short note we observe that the recent examples of derived-equivalent Calabi-Yau 3-folds with different fundamental groups also have different Brauer groups, using a little topological K-theory.