The Golod property for Stanley-Reisner rings in varying characteristic

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.

13 pages. Minor corrections, one simplified proof. To appear in J. Pure and applied Alg

References in corpus (2)

• Algebra+Homotopy=Operad
• On the multigraded Hilbert and Poincaré-Betti series and the Golod property of monomial rings

Cited by in corpus (2)

• Fat wedge filtrations and decomposition of polyhedral products
• A-infinity resolutions and the Golod property for monomial rings