The Serre-Swan Theorem in supergeometry
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908990356586496 |
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| author | Morye, Archana S. Soman, Abhay Devichandrika, V. |
| author_facet | Morye, Archana S. Soman, Abhay Devichandrika, V. |
| contents | We show the analogue of the Serre-Swan theorem in a context of supergeometry. This theorem gives an equivalence of the category of locally free supersheaves of bounded rank over locally ringed superspace with the category of finitely generated super projective modules over its coordinate superring, under the assumptions that every locally free supersheaf is generated by global sections and it is acyclic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01249 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Serre-Swan Theorem in supergeometry Morye, Archana S. Soman, Abhay Devichandrika, V. Algebraic Geometry Mathematical Physics 14M30, 58A50, 14A22 We show the analogue of the Serre-Swan theorem in a context of supergeometry. This theorem gives an equivalence of the category of locally free supersheaves of bounded rank over locally ringed superspace with the category of finitely generated super projective modules over its coordinate superring, under the assumptions that every locally free supersheaf is generated by global sections and it is acyclic. |
| title | The Serre-Swan Theorem in supergeometry |
| topic | Algebraic Geometry Mathematical Physics 14M30, 58A50, 14A22 |
| url | https://arxiv.org/abs/2503.01249 |