The Bounded t-Structure of Triangulated Categories and Hereditary Abelian Categories

The t-structure of triangulated categories is the promotion of the torsion theory of abelian categories on the triangulated categories,which plays an important role in the study of the algebraic geometry.The heart of the bounded t-structure of triangulated categories is studied in this paper.It is proved that any given bounded t-stucture(D≤0,D≥0) on D satisfies that X∈D≤0,or X∈D≥1,for any indecomposable object X in D.Then the heart of the certain t-structure is hereditary.Moreover,if(T,F) is the splited torsion theory of the hereditary abelian category A,then the heart of the bounded t-structure on the bounded derived category Db(A) deduced by(T,F) is also hereditary abelian category.