Séminaire de Géométrie Algébrique et Singularités

An introduction to the theory of valuations.

by Mark Spivakovsky (IMT et CNRS)

Salle Pellos (bât. 1R2, Salle 207) (IMT)

Salle Pellos (bât. 1R2, Salle 207)



The purpose of this talk is to provide an introduction and some background to the lectures of Franz-Viktor Kuhlmann on September 21 and Jonsei Novacoski on September 28. We will start with the definition of valuation and explain the connection between valuations and the problem of resolution of singularities in algebraic geometry (the local uniformization problem). We will go on to discuss the notions of henselian and tame valued fields as well as that of key polynomials and their geometric interpretation, and the notion of defect of an extension of valued fields.