Noncatenary splinters in prime characteristic
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909059084451840 |
|---|---|
| author | Loepp, S. Simpson, Austyn |
| author_facet | Loepp, S. Simpson, Austyn |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noncatenary splinters in prime characteristic Loepp, S. Simpson, Austyn Commutative Algebra 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. |
| title | Noncatenary splinters in prime characteristic |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2401.00925 |