On the Frobenius Complexity of Stanley-Reisner Rings

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 Àlvarez Montaner, Boix and Zarzuela. Our result settles an open question mentioned by Àlvarez Montaner in [1].