Back to Commutative Algebra Seminar: Fall 2023
Commutative Algebra Seminar
Date: Friday, Oct 27, 2023
Time: 2:00PM - 3:00PM
Location: LCB 323
Anna Brosowsky
University of Michigan
Title |
Cartier algebras through the lens of p-families |
Abstract |
A Cartier subalgebra of a prime characteristic commutative ring R is an associated non-commutative ring of operators on R that play nicely with the Frobenius map. When R is regular, its Cartier subalgebras correspond exactly with sequences of ideals called F-graded systems. One special subclass of F-graded system is called a p-family; these appear in numerical applications such as the Hilbert-Kunz multiplicity and the F-signature. In this talk, I will discuss how to characterize some properties of a Cartier subalgebra in terms of its F-graded system. I will further present a way to construct, for an arbitrary F-graded system, a closely related p-family with especially nice properties. |
Commutative Algebra