F-Signature and Relative Hilbert-Kunz Multiplicity Revisited

F-Signature and Relative Hilbert-Kunz Multiplicity Revisited

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Kevin Tucker, Princeton University
Fine Hall 322

In this talk, building on an observation of Yao, we will sketch a partial answer to a question of Watanabe and Yoshida by showing that the F-signature and relative Hilbert-Kunz multiplicity (for cyclic modules) coincide. The method of proof also suggests a number of generalizations of F-signature which we will present as time allows.