Point Objects and Derived Equivalences of Twisted Derived Categories of Abelian Varieties

Abstract

We study the notion of $1$-twisted semi-homogeneous vector bundles on ${\mathbb{G}}_m$-gerbes over abelian varieties, and classify point objects in the twisted derived categories of abelian varieties. As an application, we classify the twisted Fourier-Mukai partners of abelian varieties.