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This is a Quantitative Study study.

October 8, 2025Open Access

F-injectivity does not imply F-fullness in normal domains

Key Points

F-injectivity does not imply F-fullness in some three-dimensional local geometrically normal domains.
Specific examples include two-dimensional local geometrically normal domains that are F-injective but not F-anti-nilpotent.
The study focuses on the behavior of F-injectivity during purely inseparable finite base changes.
The findings challenge existing assumptions about the relationships between different properties of normal domains.

Abstract

We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are F-injective but not F-full. Along the way, we find examples of two-dimensional local geometrically normal domains which are F-injective but not F-anti-nilpotent. A crucial theme of our constructions is the behavior of F-injectivity along a purely inseparable finite base change.

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Cite This Study

Stefani et al. (Sat,) studied this question.

synapsesocial.com/papers/68e6d7971ffa7aa7d63d1906 https://doi.org/https://doi.org/10.48550/arxiv.2506.00646

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