English

Abelian 1-Calabi-Yau Categories

Category Theory 2008-02-26 v2

Abstract

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.

Keywords

Cite

@article{arxiv.math/0703457,
  title  = {Abelian 1-Calabi-Yau Categories},
  author = {Adam-Christiaan van Roosmalen},
  journal= {arXiv preprint arXiv:math/0703457},
  year   = {2008}
}

Comments

12 pages, as accepted by the International Mathematics Research Notices

R2 v1 2026-07-22T17:52:43.387Z