Geodesic
t-stabilities and t-structures on triangulated categories
Izvestiya. Mathematics , Tome 68 (2004) no. 4, pp. 749-781.

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We suggest a new concept of t-stability in a triangulated category. It generalizes the stability data introduced by Bridgeland [6]. We study some links between t-stabilities and t-structures and obtain a complete classification of t-stabilities and bounded t-structures on the derived categories of coherent sheaves on the projective line and on an elliptic curve. 
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A. L. Gorodentsev; S. A. Kuleshov; A. N. Rudakov. t-stabilities and t-structures on triangulated categories. Izvestiya. Mathematics , Tome 68 (2004) no. 4, pp. 749-781. http://geodesic.mathdoc.fr/item/IM2_2004_68_4_a3/

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