BIMSA > Commutative Algebra Seminar in Beijing h-functions of local rings of characteristic p
h-functions of local rings of characteristic p
Organizers
Ming Fang , Manolis Tsakiris , Bei Hui Yuan
Speaker
Cheng Meng
Time
Friday, November 15, 2024 9:30 AM - 11:30 AM
Venue
AMSS-N208
Abstract
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.