Noncatenary splinters in prime characteristic

S. Loepp; Austyn Simpson

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arXiv · 2401.00925

Noncatenary splinters in prime characteristic

S. Loepp·Austyn Simpson

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Abstract

We construct a local Noetherian splinter (in fact, a weakly $F$-regular domain) in prime characteristic which is not catenary, which we view as an analogue of a theorem of Ogoma in equal characteristic zero. Moreover, we construct a weakly $F$-regular local UFD which is not Cohen-Macaulay. Both of these examples are obtained via finding sufficient conditions ensuring that a complete local ring of prime characteristic is the completion of some weakly $F$-regular local domain, which we expect to be of independent interest.

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S. Loepp, Austyn Simpson. 2024-01-01. Noncatenary splinters in prime characteristic. https://arxiv.org/abs/2401.00925

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