On the generators of coordinate algebras of affine ind-varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911095171579904 |
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| author | Chernov, Alexander |
| author_facet | Chernov, Alexander |
| contents | In this paper we study the structure of the coordinate ring of an affine ind-variety. We prove that any coordinate ring of an affine ind-variety which is not isomorphic to an affine algebraic variety does not have a countable set of generators. Also we prove that coordinate rings of affine ind-varieties have an everywhere dense subspace of countable dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22408 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the generators of coordinate algebras of affine ind-varieties Chernov, Alexander Algebraic Geometry Commutative Algebra In this paper we study the structure of the coordinate ring of an affine ind-variety. We prove that any coordinate ring of an affine ind-variety which is not isomorphic to an affine algebraic variety does not have a countable set of generators. Also we prove that coordinate rings of affine ind-varieties have an everywhere dense subspace of countable dimension. |
| title | On the generators of coordinate algebras of affine ind-varieties |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2507.22408 |