## “Bulletin Board”

School of Mathematics - September 22, 2007

### Lecture

#### Valuation Theory and Binomial IdealsBernard Teissier CNRS, France and Institut Mathematiques de Jussieu, FranceSeptember 24, 2007

Valuation Theory and Binomial Ideals

Bernard Teissier,
CNRS, France
and
Institut Mathematiques de Jussieu, France

Abstract

Let $R$ be a local noetherian integral domain with an algebraically closed residue field. Let $R_{\nu}$ be the ring of a valuation of the field of fractions $K$ of $R$. Assume that $R_{\nu}$ dominates $R$ and $R/\frak{m}=R_{\nu}/\frak{m}_{\nu}$. The associated graded ring of $R$ with respect to $\nu$ is a quotient of a polynomial ring in a well-ordered set of indeterminates by a prime binomial ideal. It is of finite Krull dimension. A suitable completion of the ring $R$ appears as a deformation of a completion at the origin of this graded ring. Some consequences will be shown.

Information:

 Date: Monday, September 24, 2007, 17:00-18:00 Place: Niavaran Bldg., Niavaran Square, Tehran, Iran