On some properties of the asymptotic Samuel function

Abstract

The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.

We thank the referee for several useful suggestions and constructive criticism of the paper. The initial part of the proof of Theorem 5.5 has been changed. To appear in Math. Nach. 22 pages