1. Uniform arithmetic in local rings via ultraproducts
- Author
-
Adams, Clay, Cantor, Francesca, Gashi, Anese, Mujevic, Semir, Park, Sejin, Simpson, Austyn, and Zomback, Jenna
- Subjects
Mathematics - Commutative Algebra - Abstract
We reinterpret various properties of Noetherian local rings via the existence of some $n$-ary numerical function satisfying certain uniform bounds. We provide such characterizations for seminormality, weak normality, generalized Cohen-Macaulayness, and $F$-purity, among others. Our proofs that such numerical functions exist are nonconstructive and rely on the transference of the property in question from a local ring to its ultrapower or catapower., Comment: Written during the 2023 SMALL REU at Williams College. 19 pages. Comments welcome more...
- Published
- 2023