A classification theorem for t-structures

Abstract

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, a large class of 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 generalizes 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 [16]. 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 [22,20].