The strong uniform Artin-Rees property in codimension one

Abstract

The purpose of this paper is to prove the following theorem of uniform Artin-Rees properties: Let $A$ be an excellent (in fact J-2) ring and let $N\subset M$ be two finitely generated $A$-modules such that $\dim (M/N)\le 1$. Then there exists an integer $s\ge 1$ such that, for all integers $n\ge s$ and for all ideals $I$ of $A$, $I^{n}M\cap N=I^{n-s}(I^{s}M\cap N)$.

14 pages, Latex