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