On Gluing Data, Finite Ringed Spaces and schemes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915814595100672 |
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| author | Fioresi, Rita Simonetti, Angelica Zanchetta, Ferdinando |
| author_facet | Fioresi, Rita Simonetti, Angelica Zanchetta, Ferdinando |
| contents | From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link important geometric objects, such as differentiable manifolds or schemes, to certain finite ringed spaces arising from sheaves on 2 dimensional semisimplicial sets, thus opening the door to their applications in fields such as discrete differential geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21184 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Gluing Data, Finite Ringed Spaces and schemes Fioresi, Rita Simonetti, Angelica Zanchetta, Ferdinando Category Theory From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link important geometric objects, such as differentiable manifolds or schemes, to certain finite ringed spaces arising from sheaves on 2 dimensional semisimplicial sets, thus opening the door to their applications in fields such as discrete differential geometry. |
| title | On Gluing Data, Finite Ringed Spaces and schemes |
| topic | Category Theory |
| url | https://arxiv.org/abs/2602.21184 |