A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEs
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914510044921856 |
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| author | Savage, Rhiannon |
| author_facet | Savage, Rhiannon |
| contents | Proving representability of derived moduli stacks of solutions to non-linear elliptic partial differential equations generally requires significant analytic machinery. In this paper, we instead show that representability naturally follows from an Artin-Lurie style representability theorem. This necessitates the development of a new model for derived differential geometry using an extension of $C^\infty$-rings that we call $C^\infty$-bornological rings. This new theory embeds into the theory of derived bornological geometry recently proposed by Ben-Bassat, Kelly, and Kremnizer. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24164 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEs Savage, Rhiannon Algebraic Geometry Category Theory Differential Geometry 14D23, 18F20, 18N60 Proving representability of derived moduli stacks of solutions to non-linear elliptic partial differential equations generally requires significant analytic machinery. In this paper, we instead show that representability naturally follows from an Artin-Lurie style representability theorem. This necessitates the development of a new model for derived differential geometry using an extension of $C^\infty$-rings that we call $C^\infty$-bornological rings. This new theory embeds into the theory of derived bornological geometry recently proposed by Ben-Bassat, Kelly, and Kremnizer. |
| title | A Bornological Perspective on the Representability of Derived Moduli Stacks of Solutions to PDEs |
| topic | Algebraic Geometry Category Theory Differential Geometry 14D23, 18F20, 18N60 |
| url | https://arxiv.org/abs/2604.24164 |