The co-stability manifold of a triangulated category

Jorgensen, Peter and Pauksztello, David (2013) The co-stability manifold of a triangulated category. Glasgow Mathematical Journal, 55 (1). pp. 161-175. ISSN 0017-0895

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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 Dc(k[X]/(X2)), 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 Dc(k[X]/(X2)) is ℂ.

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Journal Article
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Glasgow Mathematical Journal
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06 Oct 2017 19:38
Last Modified:
18 Sep 2023 01:15