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On the Frobenius Complexity of Stanley-Reisner Rings

2019/11/14 by Ilioaea, Irina
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.06417

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 -∞ 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≥ 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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