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arXiv · 1911.06417

On the Frobenius Complexity of Stanley-Reisner Rings

Irina Ilioaea
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Abstract

The Frobenius complexity of a local ring $R$ measures asymptotically the abundance of Frobenius operators of order $e$ on the injective hull of the residue field of $R$. It is known that, for Stanley-Reisner rings, the Frobenius complexity is either $-\infty$ or $0$. This invariant is determined by the complexity sequence $\{c_ e\}_e $ of the ring of Frobenius operators on the injective hull of the residue field. We will show that $\{c_ e\}_e $ is constant for $e\geq 2,$ generalizing work of Alvarez Montaner, Boix and Zarzuela. Our result settles an open question mentioned by Alvarez Montaner in one of his papers.

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Irina Ilioaea. 2019-11-14. On the Frobenius Complexity of Stanley-Reisner Rings. https://arxiv.org/abs/1911.06417

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