$F$-injectivity does not imply $F$-fullness in normal domains
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.
Authors
- Alessandro De Stefani (ORCID: https://orcid.org/0000-0003-3094-956X)
- Thomas Polstra (ORCID: https://orcid.org/0000-0003-0856-9296)
- Austyn Simpson
Institutions
- University of Alabama (US)
- Bates College (US)
- University of Genoa (IT)
Publication Details
- Journal
- Épijournal de Géométrie Algébrique
- Published
- 2026-10-30
- DOI
- https://doi.org/10.46298/epiga.2026.16680
- Primary Topic
- Commutative Algebra and Its Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni