Gorodentsev, A. L.; Kuleshov, S. A.; Rudakov, A. N. \(t\)-stabilities and \(t\)-structures on triangulated categories. (English. Russian original) Zbl 1062.18009 Izv. Math. 68, No. 4, 749-781 (2004); translation from Izv. Ross. Akad. Nauk Ser. Mat. 68, No. 4, 117-150 (2004). Summary: We suggest a new concept of \(t\)-stability in a triangulated category. It generalizes the stability data introduced by T. Bridgeland [“Stability conditions on triangulated categories”, xxx.lanl.gov/abs/math.AG/0212237 (2003)]. 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. Cited in 3 ReviewsCited in 23 Documents MSC: 18E30 Derived categories, triangulated categories (MSC2010) PDFBibTeX XMLCite \textit{A. L. Gorodentsev} et al., Izv. Math. 68, No. 4, 749--781 (2004; Zbl 1062.18009); translation from Izv. Ross. Akad. Nauk Ser. Mat. 68, No. 4, 117--150 (2004) Full Text: DOI