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THE CO-STABILITY MANIFOLD OF A TRIANGULATED CATEGORY

Published online by Cambridge University Press:  02 August 2012

PETER JØRGENSEN  and
DAVID PAUKSZTELLO
PETER JØRGENSEN
Affiliation:
School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom e-mail: peter.jorgensen@ncl.ac.uk
DAVID PAUKSZTELLO
Affiliation:
Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und Physik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany e-mail: pauk@math.uni-hannover.de
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Abstract

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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.

Keywords

18E30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 1 , January 2013 , pp. 161 - 175
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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