Seminar

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For a Noetherian local ring R of characteristic p, we will study a multiplicity-like object called h-function. It is a function of a real variable s that estimates the asymptotic behavior of the sum of an ordinary power and a Frobenius power. The h-function of a local ring can be viewed as a mixture of the Hilbert-Samuel multiplicity and the Hilbert-Kunz multiplicity. In this talk, we will focus on how h-function recovers other invariants in characteristic p, and some open problems related to h-function. We will also talk about properties of h-function, including convexity, differentiability and additivity.