Sur la fonction de Hilbert-Samuel des clôtures intégrales des puissances d'idéaux engendrés par un système de paramètres. (On the Hilbert-Samuel function of the integral closure of powers of ideals generated by a system of parameters) (Q913865)

Let A be a local excellent Noetherian ring of dimension d and I an ideal generated by a system of parameters. First, the comparison between the I- adic filtration and the filtration \(\overline{I^ n}\) for n large, where \(\overline{I^ n}\) is the integral closure of \(I^ n\) is made. Then, in the case when additionally A is a domain, the authors compare the Hilbert-Samuel functions \(\lg(A/I^ n)\) and \(\lg(A/\overline{I^ n})\); they study when they have the same coefficient of \(n^{d-1}\).