Plus-pure thresholds of some cusp-like singularities in mixed characteristic
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911122197577728 |
|---|---|
| author | Cai, Hanlin Pande, Suchitra Quinlan-Gallego, Eamon Schwede, Karl Tucker, Kevin |
| author_facet | Cai, Hanlin Pande, Suchitra Quinlan-Gallego, Eamon Schwede, Karl Tucker, Kevin |
| contents | Log-canonical and $F$-pure thresholds of pairs in equal characteristic admit an analog in the recent theory of singularities in mixed characteristic, which is known as the plus-pure threshold. In this paper we study plus-pure thresholds for singularities of the form $p^a + x^b \in {\bf Z}_p [[ x ]]$, showing that in a number of cases this plus-pure threshold agrees with the $F$-pure threshold of the singularity $t^a + x^b \in {\bf F}_p [[ t, x ]]$. We also discuss a few other sporadic examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Plus-pure thresholds of some cusp-like singularities in mixed characteristic Cai, Hanlin Pande, Suchitra Quinlan-Gallego, Eamon Schwede, Karl Tucker, Kevin Algebraic Geometry Commutative Algebra Log-canonical and $F$-pure thresholds of pairs in equal characteristic admit an analog in the recent theory of singularities in mixed characteristic, which is known as the plus-pure threshold. In this paper we study plus-pure thresholds for singularities of the form $p^a + x^b \in {\bf Z}_p [[ x ]]$, showing that in a number of cases this plus-pure threshold agrees with the $F$-pure threshold of the singularity $t^a + x^b \in {\bf F}_p [[ t, x ]]$. We also discuss a few other sporadic examples. |
| title | Plus-pure thresholds of some cusp-like singularities in mixed characteristic |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2501.07528 |