$C^\infty$-superrings and $C^\infty$-superschemes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915641289605120 |
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| author | Olarte, Cristian Danilo Rizzo, Pedro Torres-Gomez, Alexander |
| author_facet | Olarte, Cristian Danilo Rizzo, Pedro Torres-Gomez, Alexander |
| contents | This paper develops a theory of $C^\infty$-superrings and their associated $C^\infty$-superschemes. We prove a key equivalence between the category of fair affine $C^\infty$-superschemes and the category of fair $C^\infty$-superrings. We place special emphasis on split $C^\infty$-superrings, which generalize the function algebras of supermanifolds and serve as building blocks for more complex, non-split structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C^\infty$-superrings and $C^\infty$-superschemes Olarte, Cristian Danilo Rizzo, Pedro Torres-Gomez, Alexander Algebraic Geometry Differential Geometry Rings and Algebras This paper develops a theory of $C^\infty$-superrings and their associated $C^\infty$-superschemes. We prove a key equivalence between the category of fair affine $C^\infty$-superschemes and the category of fair $C^\infty$-superrings. We place special emphasis on split $C^\infty$-superrings, which generalize the function algebras of supermanifolds and serve as building blocks for more complex, non-split structures. |
| title | $C^\infty$-superrings and $C^\infty$-superschemes |
| topic | Algebraic Geometry Differential Geometry Rings and Algebras |
| url | https://arxiv.org/abs/2508.09900 |