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arXiv · 2312.17391

Uniform arithmetic in local rings via ultraproducts

Clay Adams·Francesca Cantor·Anese Gashi·Semir Mujevic·Sejin Park·Austyn Simpson·Jenna Zomback
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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.

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Clay Adams, Francesca Cantor, Anese Gashi, Semir Mujevic, Sejin Park, Austyn Simpson, Jenna Zomback. 2023-12-28. Uniform arithmetic in local rings via ultraproducts. https://arxiv.org/abs/2312.17391

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