  In this paper, we show all k-linear abelian 1-Calabi-Yau categories over an
algebraically closed field k are derived equivalent to either the category of
coherent sheaves on an elliptic curve, or to the finite dimensional
representations of k[[t]]. Since all abelian categories derived equivalent with
these two are known, we obtain a classification of all k-linear abelian
1-Calabi-Yau categories up to equivalence.
