A Characterization of Closure Operations That Induce Big Cohen-Macaulay Modules

TL;DR

This paper establishes axioms for closure operations that produce balanced big Cohen-Macaulay modules over complete local domains, and shows the equivalence between such modules and these closure operations.

Contribution

It introduces a set of axioms characterizing closure operations that generate big Cohen-Macaulay modules and proves their equivalence.

Findings

Axioms for closure operations are sufficient for generating big Cohen-Macaulay modules.

Existence of a big Cohen-Macaulay module implies the existence of a closure operation satisfying the axioms.

The paper provides a characterization linking closure operations and Cohen-Macaulay modules.

Abstract

The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module B over a complete local domain R. Conversely, we show that if such a B exists over R, then there exists a closure operation that satisfies the given axioms.