arXiv subjects

Jean-Christophe San Saturnino

Publications and source records attributed to Jean-Christophe San Saturnino.

3 recordsLinked to original sources

arXiv2016

Ramification theory and key polynomials

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 associated to the extension of the valuation. More precisely, the order of this group can be expressed in terms of a product of a power of the characteristic of the residue field of the valuation and the effective degrees of the key polynomials. We also give a condition on the order of the ramification group so that there is no limit key polynomials for a valuation of rank one. This condition also allow us to have a monomialization theorem.

math.AG↗

arXiv2014

Defect of an extension, key polynomials and local uniformization

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 consequence, we obtain a local uniformization theorem for valuations of rank 1 centered on an equicharacteristic quasi-excellent local domain satisfying some inductive assumptions of lack of defect.

math.AG↗

arXiv2013

Uniformisation locale des schémas quasi-excellents de caractéristique nulle

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.

math.AG↗