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arXiv · 1504.05037

The Golod property for Stanley-Reisner rings in varying characteristic

Lukas Katthän
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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.

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Lukas Katthän. 2015-04-20. The Golod property for Stanley-Reisner rings in varying characteristic. https://doi.org/10.1016/j.jpaa.2015.11.005

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