Épijournal de Géométrie Algébrique· 2026Q1
$F$-injectivity does not imply $F$-fullness in normal domains
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- 2026year
Short summary
We construct Noetherian, 3D, local, geometrically normal domains of prime characteristic that are $F$-injective but not $F$-full.
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Key points
- Constructed examples of Noetherian, 3D, local, geometrically normal domains.
- These domains are $F$-injective but not $F$-full.
- The constructions are of prime characteristic.
- Analyzed the behavior of $F$-injectivity under purely inseparable finite base change.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Épijournal de Géométrie Algébrique, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics