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arXiv · 2506.00646

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

Alessandro De Stefani·Thomas Polstra·Austyn Simpson
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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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Alessandro De Stefani, Thomas Polstra, Austyn Simpson. 2025-05-31. $F$-injectivity does not imply $F$-fullness in normal domains. https://arxiv.org/abs/2506.00646

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