THE CO-STABILITY MANIFOLD OF A TRIANGULATED CATEGORY
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Publication:4899937
DOI10.1017/S0017089512000420zbMATH Open1263.18007arXiv1109.4006MaRDI QIDQ4899937
Author name not available (Why is that?)
Publication date: 10 January 2013
Published in: (Search for Journal in Brave)
Abstract: Stability conditions on triangulated categories were introduced by Bridgeland as a 'continuous' generalisation of t-structures. The set of locally-finite stability conditions on a triangulated category is a manifold which has been studied intensively. However, there are mainstream triangulated categories whose stability manifold is the empty set. One example is the compact derived category of the dual numbers over an algebraically closed field. This is one of the motivations in this paper for introducing co-stability conditions as a 'continuous' generalisation of co-t-structures. Our main result is that the set of nice co-stability conditions on a triangulated category is a manifold. In particular, we show that the co-stability manifold of the compact derived category of the dual numbers is the complex numbers.
Full work available at URL: https://arxiv.org/abs/1109.4006
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