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Hilbert coefficients of good I-Filtrations of modules

Le Xuan Dung

Abstract

Let $M$ be a finitely generated module of dimention d over a Noetherian local ring (A,m) and I an m-primary ideal. Let be a pair of good I-filtrations F and F' of M. We show that the Hilbert coefficients e_i(F) are bounded below and above in terms of i, e_0(F'),...,e_i(F'), and reduction numbers of F and F', for all i \ge 1.

Hilbert coefficients of good I-Filtrations of modules

Abstract

Let be a finitely generated module of dimention d over a Noetherian local ring (A,m) and I an m-primary ideal. Let be a pair of good I-filtrations F and F' of M. We show that the Hilbert coefficients e_i(F) are bounded below and above in terms of i, e_0(F'),...,e_i(F'), and reduction numbers of F and F', for all i \ge 1.
Paper Structure (3 sections, 11 theorems, 60 equations)

This paper contains 3 sections, 11 theorems, 60 equations.

Table of Contents

  1. Introduction
  2. Hilbert coefficients and local cohomomology modules
  3. Main results

Key Result

Lemma 2.1

(DH2) Let $E$ be a finitely generated graded $R$-module of dimension $d\ge 1$. Put Then we have

Theorems & Definitions (19)

  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Lemma 2.6
  • proof
  • Lemma 3.1
  • ...and 9 more