On the dimension of discrete valuations of k((X1,...,Xn))

Details On the dimension of discrete valuations of k((X1,...,Xn)) On the dimension of discrete valuations of k((X1,...,Xn))

2000-11-15

arxiv.org/abs/math/0011096v1

C. R. Acad. Sci. Paris, S\'erie I, t. 333, p. 27-32, 2001

Mathematics

Commutative Algebra

5 pages

Scientific paper

Let $v$ be a rank-one discrete valuation of the field $k((\X))$. We know,
after \cite{Bri2}, that if $n=2$ then the dimension of $v$ is 1 and if $v$ is
the usual order function over $k((\X))$ its dimension is $n-1$. In this paper
we prove that, in the general case, the dimension of a rank-one discrete
valuation can be any number between 1 and $n-1$.

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