On the boundedness of $k$-algebra homomorphisms between $k$-affinoid algebras
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913857477279744 |
|---|---|
| author | Yoshikawa, Shou |
| author_facet | Yoshikawa, Shou |
| contents | Let $k$ be a complete non-archimedean non-trivial valued field. In this paper, we investigate whether every $k$-algebra homomorphism between $k$-affinoid algebras is automatically bounded. We show that this property holds if and only if either $|k^\times|^\mathbb{Q} = \mathbb{R}_{>0}$ holds, or $k$ has positive characteristic and is $F$-finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the boundedness of $k$-algebra homomorphisms between $k$-affinoid algebras Yoshikawa, Shou Algebraic Geometry Let $k$ be a complete non-archimedean non-trivial valued field. In this paper, we investigate whether every $k$-algebra homomorphism between $k$-affinoid algebras is automatically bounded. We show that this property holds if and only if either $|k^\times|^\mathbb{Q} = \mathbb{R}_{>0}$ holds, or $k$ has positive characteristic and is $F$-finite. |
| title | On the boundedness of $k$-algebra homomorphisms between $k$-affinoid algebras |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2505.18428 |