Globalizing F-invariants
  In this paper we define and study the global Hilbert-Kunz multiplicity and the global F-signature of prime characteristic rings which are not necessarily local. Our techniques are made meaningful by extending many known theorems about Hilbert-Kunz multiplicity and F-signature to the non-local case. 
Alessandro De Stefani, Thomas Polstra, Yongwei Yao
math.AC