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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn003, 20 pages, doi:10.1093/imrn/rnn003 published on February 15, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Abelian 1-Calabi–Yau Categories

Adam-Christiaan van Roosmalen

Hasselt University, Research Group Algebra, Agoralaan, Gebouw D, B-3590 Diepenbeek, Belgium

Correspondence: Correspondence to be sent to: AdamChristiaan.vanRoosmalen{at}UHasselt.be

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.


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