Uniformisation locale des schémas quasi-excellents de caractéristique nulle

Abstract

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.

in French

References in corpus (3)

• Desingularization of quasi-excellent schemes in characteristic zero
• Extending a valuation centered in a local domain to the formal completion
• Resolution of Singularities of Arithmetical Threefolds II

Cited by in corpus (2)

• Defect of an extension, key polynomials and local uniformization
• Ramification theory and key polynomials