Upper semi-continuity of the Hilbert-Kunz multiplicity

Abstract

We prove that the Hilbert-Kunz multiplicity is upper semi-continuous in F-finite rings and algebras of essentially finite type over an excellent local ring.

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• Equimultiplicity in Hilbert-Kunz theory
• Bertini Theorems for $F$-signature and Hilbert-Kunz multiplicity
• Local Okounkov bodies and limits in prime characteristic
• Global Frobenius Betti numbers and F-splitting ratio
• Globalizing F-invariants