Continuity of differential operators for nonarchimedean Banach algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909579075387392 |
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| author | Rączka, Feliks |
| author_facet | Rączka, Feliks |
| contents | Given a nonarchimedean field $K$ and a commutative, noetherian, Banach $K$-algebra $A$, we study continuity of $K$-linear differential operators (in the sense of Grothendieck) between finitely generated Banach $A$-modules. When $K$ is of characteristic zero we show that every such operator is continuous if and only if $A/\mathfrak{m}$ is a finite extension of $K$ for every maximal ideal $\mathfrak{m}\subset A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuity of differential operators for nonarchimedean Banach algebras Rączka, Feliks Algebraic Geometry Functional Analysis 14F10. 14G22, 46S10 Given a nonarchimedean field $K$ and a commutative, noetherian, Banach $K$-algebra $A$, we study continuity of $K$-linear differential operators (in the sense of Grothendieck) between finitely generated Banach $A$-modules. When $K$ is of characteristic zero we show that every such operator is continuous if and only if $A/\mathfrak{m}$ is a finite extension of $K$ for every maximal ideal $\mathfrak{m}\subset A$. |
| title | Continuity of differential operators for nonarchimedean Banach algebras |
| topic | Algebraic Geometry Functional Analysis 14F10. 14G22, 46S10 |
| url | https://arxiv.org/abs/2504.10209 |