A differential-algebraic criterion for obtaining a small maximal Cohen-Macaulay module

TL;DR

This paper proves that certain derivations imply the existence of small maximal Cohen-Macaulay modules in specific three-dimensional rings in positive characteristic, advancing the understanding of Hochster's conjecture.

Contribution

It introduces a differential-algebraic criterion linking derivations to the existence of small MCM modules in three-dimensional rings in positive characteristic.

Findings

F-invariant, differentiable derivations imply Hochster's small MCM conjecture.

Any three-dimensional pseudo-graded ring in positive characteristic satisfies the conjecture.

Establishes a new criterion for the existence of small MCM modules.

Abstract

We show how for a three-dimensional complete local ring in positive characteristic, the existence of an F-invariant, differentiable derivation implies Hochster's small MCM conjecture. As an application we show that any three-dimensional pseudo-graded ring in positive characteristic satisfies Hochster's small MCM conjecture.