$F$-intersection flatness of dagger and Berkovich affinoid algebras
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909891436740608 |
|---|---|
| author | Datta, Rankeya Garzella, Jack J Tucker, Kevin |
| author_facet | Datta, Rankeya Garzella, Jack J Tucker, Kevin |
| contents | We show, using the techniques developed in arXiv:2504.06444 and arXiv:2305.11139, that dagger algebras and Tate algebras in the sense of Berkovich in prime characteristic $p > 0$ have intersection flat Frobenius. Equivalently, if $S$ is such a ring, then $S^{1/p}$ is a flat and Mittag-Leffler $S$-module. As a consequence, we deduce that any ideal-adic completion of a reduced ring that is essentially of finite type over a dagger algebra or a Berkovich Tate algebra in prime characteristic has big test elements from tight closure theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00753 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $F$-intersection flatness of dagger and Berkovich affinoid algebras Datta, Rankeya Garzella, Jack J Tucker, Kevin Commutative Algebra Algebraic Geometry Number Theory 13A35, 14G22 We show, using the techniques developed in arXiv:2504.06444 and arXiv:2305.11139, that dagger algebras and Tate algebras in the sense of Berkovich in prime characteristic $p > 0$ have intersection flat Frobenius. Equivalently, if $S$ is such a ring, then $S^{1/p}$ is a flat and Mittag-Leffler $S$-module. As a consequence, we deduce that any ideal-adic completion of a reduced ring that is essentially of finite type over a dagger algebra or a Berkovich Tate algebra in prime characteristic has big test elements from tight closure theory. |
| title | $F$-intersection flatness of dagger and Berkovich affinoid algebras |
| topic | Commutative Algebra Algebraic Geometry Number Theory 13A35, 14G22 |
| url | https://arxiv.org/abs/2511.00753 |