h-function of local rings of characteristic p
Organizers
Speaker
Cheng Meng
Time
Thursday, December 26, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
The local theory of singularities in characteristic p is an important part in commutative algebra. They are deeply connected to singularities in characteristic 0 like the KLT singularities and log canonical singularities. Singularities in characteristic p can be described using the Frobenius map and language of commutative algebra; we use various concepts (like F-regularity and tight closure) and numerical invariants (like Hilbert Kunz multiplicity and F-signature) to characterize them. In this talk, we will mention the relationship between singularities in characteristic 0 and characteristic p. We will then focus on the numerical invariants, especially the Hilbert-Kunz multiplicity. In particular, we will develop a new numerical invariant, called the h-function, which captures many other numerical invariants.