Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Resolutions of Koszul complexes and applications

Tony J. Puthenpurakal

Abstract

In this paper we consider projective and injective resolutions of Koszul complexes and give several applications to the study of Koszul homology modules.

Resolutions of Koszul complexes and applications

Abstract

In this paper we consider projective and injective resolutions of Koszul complexes and give several applications to the study of Koszul homology modules.

Paper Structure

This paper contains 11 sections, 27 theorems, 65 equations.

Table of Contents

  1. introduction
  2. The construction and three spectral sequences
  3. Proof of Theorem \ref{['prop']}
  4. Proof of Theorem \ref{['hyp']}
  5. Proof of Theorem \ref{['chi']}
  6. Proof of Theorem \ref{['perfect']}
  7. Proof of Theorems \ref{['all-one']} and \ref{['growth']}
  8. Proof of Theorems \ref{['ci']} and \ref{['ci-m']}
  9. Proof of Theorems \ref{['depth']}, \ref{['cmd']} and \ref{['pdim-depth']}
  10. Proof of Theorem \ref{['hom']}
  11. Proof of Theorems \ref{['gor-cm']} and \ref{['two-add']}

Key Result

Theorem 1.1

Let $(A,\mathfrak{m} )$ be an analytically un-ramified Cohen-Macaulay local ring with embedding dimension $e$ and dimension $d$. Assume $A$ is not regular. Then the following assertions are equivalent:

Theorems & Definitions (53)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Theorem 1.5
  • Theorem 1.6
  • Theorem 1.7
  • Theorem 1.8
  • Theorem 1.9
  • Theorem 1.10
  • ...and 43 more