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We give necessary and sufficient conditions for torsion pairs in a hereditarycategory to be in bijection with $t$-structures in the bounded derived categoryof that hereditary category. We prove that the existence of a split$t$-structure with nontrivial heart in a semiconnected Krull-Schmidt categoryimplies that this category is equivalent to the derived category of ahereditary category. We construct a bijection between split torsion pairs inthe module category of a tilted algebra having a complete slice in thepreinjective component with corresponding $t$-structures. Finally, we classifysplit $t$-structures in the derived category of a hereditary algebra.

Split $t$-structures and torsion pairs in hereditary categories