| 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. In
this talk I will show that the conjecture is true for noetherian
schemes of characteristic zero. Namely, we will desingularize integral
noetherian quasi-excellent schemes over Q using desingularization of
algebraic varieties as a main input. If time permits we will also touch
functorial desingularization of such schemes, which is a much stronger
result and, in particular, automatically implies desingularization of
complex and p-adic analytic spaces. |