A classification theorem for t-structures

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We give a classification theorem for a relevant class of t-structures in triangulated categories, which includes in the case of the derived category of a Grothendieck category, the t-structures whose hearts have at most n fixed consecutive non-zero cohomologies. Moreover, by this classification theorem, we deduce the construction of the t-tree, a new technique which generalises the filtration induced by a torsion pair. At last we apply our results in the tilting context generalizing the 1-tilting equivalence proved by Happel, Reiten and Smalø [HRS96]. The last section provides applications to classical n-tilting objects, examples of t-trees for modules over a path algebra, and new developments on compatible t-structures [KeV88b], [Ke07].