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 of the ring of Frobenius operators on the injective hull of the residue field. We will show that is constant for generalizing work of Àlvarez Montaner, Boix, and Zarzuela. Our result settles an open question mentioned by Àlvarez Montaner.