Back to Commutative Algebra Seminar: Spring 2024
Commutative Algebra Seminar
Date: Friday, Feb 23, 2024
Time: 2:00PM - 3:00PM
Location: LCB 215
Austyn Simpson
University of Michigan
Title |
Weakly F-regular rings can be non-catenary |
Abstract |
Weakly F-regular rings (i.e. Noetherian rings in which all ideals are tightly closed) are among the mildest singularity types in prime characteristic commutative algebra. They are always normal, and under excellent hypotheses are Cohen-Macaulay. In this talk, I will explain how in the absence of excellence, weakly F-regular rings need not be Cohen-Macaulay or even catenary. As a consequence, we extend a theorem of Ogoma concerning the existence of non-catenary splinters of equal characteristic zero to prime characteristic. This is joint work with Susan Loepp. |
Commutative Algebra