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The co-stability manifold of a triangulated category

Lookup NU author(s): Professor Peter Jorgensen

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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 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.

Publication metadata

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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