Theorem. Let k be an algebraically closed field and A a finite dimensional k-algebra. If the derived category D^b(mod A) is equivalent to the derived category of a hereditary category, then D^b(mod A) is equivalent to the derived category of mod B, where B is a finite dimensional algebra which is hereditary or a canonical algebra.

To say that the derived category D^b(mod A) is equivalent to the derived category of a hereditary category just means that D^b(mod A) has at least one (and then many) non-trivial splitting torsion pairs.