The Golod property for Stanley-Reisner rings in varying characteristic

TL;DR

This paper demonstrates that the Golod property of Stanley-Reisner rings can vary depending on the characteristic of the base field, providing explicit examples for different prime sets.

Contribution

It constructs simplicial complexes whose Stanley-Reisner rings are Golod only in specific characteristics, showing characteristic dependence of the Golod property.

Findings

Existence of complexes with Golod property depending on characteristic

Characterization of Golod one-dimensional complexes as chordal

Explicit constructions for prescribed prime sets

Abstract

We show that the Golod property of a Stanley-Reisner ring can depend on the characteristic of the base field. More precisely, for every finite set $T$ of prime numbers we construct simplicial complexes $\Delta$ and $\Gamma$, such that $\mathbb{K}[\Delta]$ is Golod exactly in the characteristics in $T$ and $\mathbb{K}[\Gamma]$ is Golod exactly in the characteristics not in $T$. Along the way, we show that a one-dimensional simplicial complex is Golod if and only if it is chordal.