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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 that has been studied intensively. However, there are mainstream triangulated categories whose stability manifold is the empty set. One example is D-c(k[X]/(X-2)), the compact derived category of the dual numbers over an algebraically closed field k. 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 D-c(k[X]/(X-2)) is C.
Author(s): Jorgensen P, Pauksztello D
Publication type: Article
Publication status: Published
Journal: Glasgow Mathematical Journal
Year: 2013
Volume: 55
Issue: 1
Pages: 161-175
Print publication date: 02/08/2012
ISSN (print): 0017-0895
ISSN (electronic): 1469-509X
Publisher: Cambridge University Press
URL: http://dx.doi.org/10.1017/S0017089512000420
DOI: 10.1017/S0017089512000420
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