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The co-stability manifold of a triangulated category

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The co-stability manifold of a triangulated category. / Jorgensen, Peter; Pauksztello, David.
In: Glasgow Mathematical Journal, Vol. 55, No. 1, 01.2013, p. 161-175.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Jorgensen, P & Pauksztello, D 2013, 'The co-stability manifold of a triangulated category', Glasgow Mathematical Journal, vol. 55, no. 1, pp. 161-175. https://doi.org/10.1017/S0017089512000420

APA

Jorgensen, P., & Pauksztello, D. (2013). The co-stability manifold of a triangulated category. Glasgow Mathematical Journal, 55(1), 161-175. https://doi.org/10.1017/S0017089512000420

Vancouver

Jorgensen P, Pauksztello D. The co-stability manifold of a triangulated category. Glasgow Mathematical Journal. 2013 Jan;55(1):161-175. doi: 10.1017/S0017089512000420

Author

Jorgensen, Peter ; Pauksztello, David. / The co-stability manifold of a triangulated category. In: Glasgow Mathematical Journal. 2013 ; Vol. 55, No. 1. pp. 161-175.

Bibtex

@article{aa871746258147888e416591bd48bc92,
title = "The co-stability manifold of a triangulated category",
abstract = "Stability conditions on triangulated categories were introduced by Bridgeland as a {\textquoteleft}continuous{\textquoteright} 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 {\textquoteleft}continuous{\textquoteright} 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.",
author = "Peter Jorgensen and David Pauksztello",
year = "2013",
month = jan,
doi = "10.1017/S0017089512000420",
language = "English",
volume = "55",
pages = "161--175",
journal = "Glasgow Mathematical Journal",
issn = "0017-0895",
publisher = "Cambridge University Press",
number = "1",

}

RIS

TY - JOUR

T1 - The co-stability manifold of a triangulated category

AU - Jorgensen, Peter

AU - Pauksztello, David

PY - 2013/1

Y1 - 2013/1

N2 - 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.

AB - 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.

U2 - 10.1017/S0017089512000420

DO - 10.1017/S0017089512000420

M3 - Journal article

VL - 55

SP - 161

EP - 175

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - 1

ER -