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math.AG2016★ 1 cited
Ramification theory and key polynomials
Jean-Christophe San Saturnino
For a simple, normal and finite extension of a valued field, we prove that we can related the order of the ramification group of the field extension and the set of key polynomials…
math.AG2014★ 16 cited
Defect of an extension, key polynomials and local uniformization
Jean-Christophe San Saturnino
For all simple and finite extension of a valued field, we prove that its defect is the product of the effective degrees of the complete set of key polynomials associated. As a cons…
math.AG2013★ 3 cited
Uniformisation locale des schémas quasi-excellents de caractéristique nulle
Jean-Christophe San Saturnino
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…