Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Cotilting with balanced big Cohen-Macaulay modules

Isaac Bird

Abstract

Over $d$-dimensional Cohen-Macaulay rings with a canonical module, $d$-cotilting classes containing the maximal and balanced big Cohen-Macaulay modules are classified. Particular emphasis is paid to the direct limit closure of the balanced big Cohen-Macaulay modules, and the class of modules of depth $d$, which are shown to respectively be the smallest and largest such cotilting classes. Considerations are then given to the interplay between local cohomology, canonical duality and cotilting modules for the class of Gorenstein flat modules over Gorenstein local rings.

Cotilting with balanced big Cohen-Macaulay modules

Abstract

Over -dimensional Cohen-Macaulay rings with a canonical module, -cotilting classes containing the maximal and balanced big Cohen-Macaulay modules are classified. Particular emphasis is paid to the direct limit closure of the balanced big Cohen-Macaulay modules, and the class of modules of depth , which are shown to respectively be the smallest and largest such cotilting classes. Considerations are then given to the interplay between local cohomology, canonical duality and cotilting modules for the class of Gorenstein flat modules over Gorenstein local rings.

Paper Structure

This paper contains 5 sections, 16 theorems, 24 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Cotilting with balanced big Cohen-Macaulay modules
  4. Depth and cotilting
  5. Some phenomena over Gorenstein rings

Key Result

Theorem 1

Let $R$ be a $d$-dimensional Cohen-Macaulay ring with a canonical module. Then the class $\varinjlim\mathsf{CM}(R)$ is $d$-cotilting. Moreover, it is the smallest $d$-cotilting class containing the balanced big Cohen-Macaulay modules, and every cotilting module inducing $\varinjlim\mathsf{CM}(R)$ is

Theorems & Definitions (41)

  • Theorem : \ref{['bbcmcotilting']}
  • Theorem : \ref{['depthcotilting']}
  • Theorem : \ref{['cancot']}
  • Example 2.1
  • Definition 2.2
  • Lemma 2.3
  • Example 2.4
  • Theorem 2.7
  • Definition 2.9
  • Definition 2.10
  • ...and 31 more