Geodesic
THE CO-STABILITY MANIFOLD OF A TRIANGULATED CATEGORY
Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 161-175

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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.
DOI : 10.1017/S0017089512000420
Mots-clés : 18E30 
JØRGENSEN, PETER; PAUKSZTELLO, DAVID. THE CO-STABILITY MANIFOLD OF A TRIANGULATED CATEGORY. Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 161-175. doi: 10.1017/S0017089512000420
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