  We prove an embedded local uniformization theroem for a valuation centered on
a point of a quasi-excellent scheme of characteristic zero. The proof reduces
to valuations of rank 1 and consists in desingularizing the ideal formed by the
elements of infinite value and monomializing the key polynomials. We then prove
a monomialization theorem valid in all characteristic under certain conditions,
including that of non-existence of limit key polynomials, a condition that is
always satified in characteristic zero.

Algebraic Geometry