  Grothendieck proved in EGA IV that if any integral scheme of finite type over
a locally noetherian scheme X admits a desingularization, then X is
quasi-excellent, and conjectured that the converse is probably true. We prove
this conjecture for noetherian schemes of characteristic zero. Namely, starting
with the resolution of singularities for algebraic varieties of characteristic
zero, we prove the resolution of singularities for noetherian quasi-excellent
Q-schemes.
