Defect of an extension, key polynomials and local uniformization

Jean-Christophe San Saturnino (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: defect; valued fields; local uniformization; key polynomials

Domaines: Géométrie algébrique [math.AG]

Jean-Christophe San Saturnino. Defect of an extension, key polynomials and local uniformization. Journal of Algebra, 2017, 481, pp.91-119. ⟨10.1016/j.jalgebra.2017.02.023⟩. ⟨hal-01098474⟩