Continuity of Hilbert-Kunz multiplicity and F-signature

Abstract

We establish the continuity of Hilbert-Kunz multiplicity and F-signature as functions from a Cohen-Macaulay local ring $(R,\m,k)$ of prime characteristic to the real numbers at reduced parameter elements with respect to the $\m$-adic topology.

arXiv commentNew version: as pointed out by Alessandro De Stefani the main theorem for F-signature holds only if the ring is Gorenstein