  Suppose $C$ is a smooth projective curve of genus 1 over a perfect field $F$,
and $E$ is its Jacobian. In the case that $C$ has no $F$-rational points, so
that $C$ and $E$ are not isomorphic, $C$ is an $E$-torsor with a class
$\delta(C)\in H^1(\text{Gal}(\bar F/F), E(\bar F))$. Then $\delta(C)$
determines a class $\beta \in \text{Br}(E)/\text{Br}(F)$ and there is a
Fourier-Mukai equivalence of derived categories of (twisted) coherent sheaves
$\mathcal D(C) \xrightarrow{\cong} \mathcal D(E, \beta^{-1})$. We generalize
this result to higher dimensions; namely, we prove it also for torsors over
abelian varieties.
