On t-structures and torsion theories induced by compact objects

First, we show that a compact object C in a triangulated category, which satisfies suitable conditions, induces a t-structure. Second, in an abelian category we show that a complex P· of small projective objects of term length two, which satisfies suitable conditions, induces a torsion theory. In the case of module categories, using a torsion theory, we give equivalent conditions for P· to be a tilting complex. Finally, in the case of artin algebras, we give a one-to-one correspondence between tilting complexes of term length two and torsion theories with certain conditions.