  We give two proofs to the following theorem and its generalization: if a
finite dimensional algebra $A$ is derived equivalent to a smooth projective
scheme, then any derived equivalence between $A$ and another algebra $B$ is
standard, that is, isomorphic to the derived tensor functor by a two-sided
tilting complex. The main ingredients of the proofs are as follows: (1) between
the derived categories of two module categories, liftable functors coincide
with standard functors; (2) any derived equivalence between a module category
and an abelian category is uniquely factorized as the composition of a
pseudo-identity and a liftable derived equivalence; (3) the derived category of
coherent sheaves on a certain projective scheme is triangle-objective, that is,
any triangle autoequivalence on it, which preserves the the isomorphism classes
of complexes, is necessarily isomorphic to the identity functor.
