Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bass Numbers of the First Nonzero Local Cohomology Module

Andrew J. Soto Levins

Abstract

Let $R$ be a regular local ring containing a field, let $I$ be an ideal with $d=\text{ht}{I}$, and assume $\text{ht}{p}=d$ for every minimal prime $p$ of $I$. We compute the Bass numbers $μ^{0}(q,H_{I}^{d}(R))$ and $μ^{1}(q,H_{I}^{d}(R))$ for all primes $q$. We then study $μ^{2}(q,H_{I}^{d}(R))$ by considering the associated primes of $H_{I}^{d+1}(R)$.

Bass Numbers of the First Nonzero Local Cohomology Module

Abstract

Let be a regular local ring containing a field, let be an ideal with , and assume for every minimal prime of . We compute the Bass numbers and for all primes . We then study by considering the associated primes of .
Paper Structure (4 sections, 24 theorems, 104 equations)

This paper contains 4 sections, 24 theorems, 104 equations.

Table of Contents

  1. Introduction
  2. Lower Bound for Injective Dimension
  3. Main Theorem
  4. Examples

Key Result

Theorem A

Let $(R,m,k)$ be a regular local ring containing a field with $n=\dim{R}$, let $I$ be an ideal with $d=\mathop{\mathrm{ht}}\nolimits{I}$, and assume $\mathop{\mathrm{ht}}\nolimits{p}=d$ for every minimal prime $p$ of $I$. Let be the minimal injective resolution of $H_{I}^{d}(R)$. Then the following hold.

Theorems & Definitions (59)

  • Theorem A: Main Theorem
  • Definition 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Definition 2.5
  • Lemma 2.6
  • ...and 49 more