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h-functions of local rings of characteristic p

组织者

方明 , Manolis Tsakiris , 袁北彗

演讲者

孟成

时间

2024年11月15日 09:30 至 11:30

地点

AMSS-N208

摘要

For a Netherian 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 ordinary power and Frobenius power. The h-function of a local ring can be viewed as a mixture of the Hilbert-Samuel multiplicity and the Hibert-Kunz multiplicity. In this talk, we will list the properties of h-function, including existence, differentiability, additivity, and rate of growth. We will also show how h-function recovers other invariants in characteristic p, incuding the Hilbert-Kunz multiplicity, the F-signature, and the F-threshold.